Showing papers in "alexandria engineering journal in 2020"

Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative

Abstract: The present paper describes the mathematical modeling and dynamics of a novel corona virus (2019-nCoV). We describe the brief details of interaction among the bats and unknown hosts, then among the peoples and the infections reservoir (seafood market). The seafood marked are considered the main source of infection when the bats and the unknown hosts (may be wild animals) leaves the infection there. The purchasing of items from the seafood market by peoples have the ability to infect either asymptomatically or symptomatically. We reduced the model with the assumptions that the seafood market has enough source of infection that can be effective to infect people. We present the mathematical results of the model and then formulate a fractional model. We consider the available infection cases for January 21, 2020, till January 28, 2020 and parameterized the model. We compute the basic reproduction number for the data is R 0 ≈ 2.4829 . The fractional model is then solved numerically by presenting many graphical results, which can be helpful for the infection minimization.

Hall and ion slip effects on unsteady MHD free convective rotating flow through a saturated porous medium over an exponential accelerated plate

Abstract: In this paper, we have investigated the Hall and ion slip effects on the unsteady magnetohydrodynamic (MHD) free convective rotating flow over an exponentially accelerated inclined plate entrenched in a saturated porous medium with the effect of angle of inclination, variable temperature and concentration. The flow induced by the presence of heat source/sink and destructive reaction. The Laplace transform technique has been used to solve the governing equations. The effects of the non-dimensional parameters on the governing flow velocity, temperature and concentration are examined with graphical profiles. Also for engineering interest the shear stress, Nusselt number and Sherwood number are obtained analytically and discussed computationally with reference to foremost flow parameters. It is reported that the presence of magnetic field prevents the flow reversal. Angle of inclination sustains a retarding effect on velocity distribution. The present study has an immediate application in understanding the drag experienced at the heated and inclined surfaces in a seepage flow.

Investigation of cross-fluid flow containing motile gyrotactic microorganisms and nanoparticles over a three-dimensional cylinder

Abstract: Due to the variation in fluid flow behavior in various physical conditions, the presented study have been performed an investigation of cross-fluid flow containing gyrotactic microorganisms and nanoparticles on a horizontal and three-dimensional cylinder considering viscous dissipation and magnetic field. The governing equations of the problem have been solved by the Runge-Kutta fifth-order method. The aim of this study is to inspect the effects of cross fluid, microorganisms, and magnetic field, on velocity, temperature, and concentration profiles. Also, Heat flux and mass flux values for nanoparticles and microorganisms have been calculated in tabular form. In this research, the simultaneous utilization of nanoparticles with motile microorganisms in cross fluid, and three-dimensional assessment on the cylinder has been proposed as an innovation. The results show that, when the Brownian motion parameter varies from 0.1 to 0.4 and at η = 4 , the concentration of nanoparticle deduces about 80.43%. Furthermore, with the change of bioconvection Lewis number from 0.2 to 0.5, it was observed that the concentration of the microorganisms reduced about 78.38%.

Analysis of fractal fractional differential equations

Abstract: Nonlocal differential and integral operators with fractional order and fractal dimension have been recently introduced and appear to be powerful mathematical tools to model complex real world problems that could not be modeled with classical and nonlocal differential and integral operators with single order. To stress further possible application of such operators, we consider in this work an advection-dispersion model, where the velocity is considered to be 1. We consider three cases of the models, when the kernels are power law, exponential decay law and the generalized Mittag-Leffler kernel. For each case, we present a detailed analysis including, numerical solution, stability analysis and error analysis. We present some numerical simulation.

Intelligent human computer interaction based on non redundant EMG signal

Abstract: Human computer interaction plays an increasingly important role in our life. People need more intelligent, concise and efficient human-computer interaction. It is of great significance to optimize the process of human-computer interaction by using appropriate calculation methods. In order to eliminate the interference data of thumb recognition based on sEMG signal in the process of human-computer interaction, simplify the data processing, and improve the working efficiency of general equipment of sEMG signal. In the process of gesture recognition using sEMG signals generated by thumb, a method of redundant electrode determination based on variance theory is proposed. The redundancy of five groups of action signals is divided into 16 levels and visualized. By comparing the results of thumb motion recognition when different redundant channels are removed, the optimal channel combination in the process of thumb motion recognition is obtained. Finally, two kinds of classifiers suitable for sEMG signal field are selected, and the classification results are compared, and the best method of thumb motion pattern recognition is obtained.

Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model

Abstract: In this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations. As a case study, the fractal fractional Schnakenberg system is formulated with the Caputo operator (in terms of the power law), the Caputo-Fabrizio operator (with exponential decay law) and the Atangana-Baleanu fractional derivative (based on the Mittag-Liffler law). We design some algorithms for the Schnakenberg model by using the newly proposed numerical methods. In such schemes, it worth mentioning that the classical cases are recovered whenever α = 1 and β = 1 . Numerical results obtained for different fractal-order ( β ∈ ( 0 , 1 ) ) and fractional-order ( α ∈ ( 0 , 1 ) ) are also given to address any point and query that may arise.

Heat transport and nonlinear mixed convective nanomaterial slip flow of Walter-B fluid containing gyrotactic microorganisms

Abstract: Here nonlinear mixed convective nanoliquid slip flow of Walter-B fluid is addressed subject to stretched surface with gyrotactic microorganisms. The flow is generated via nonlinear stretched surface. Important slip mechanisms i.e., Brownian and thermophoresis diffusions are considered for the modeling of energy equation. Flow behavior is examined subject to nanofluid with gyrotactic microorganisms. Chemical reaction with activation energy is considered for the analysis of concentration. Suitable transformations leads to nonlinear ordinary differential system. Analytical solutions are made via built-in-Shooting and plotted graphically. The impacts of pertinent variables like viscoelastic parameter, Prandtl number, thermophoresis diffusion, Brownian motion, Chemical reaction, Schmidt number, bio-convection Lewis number, microorganisms concentration difference variable and bio-convection Peclet number on the velocity, temperature, concentration, motile density, skin friction coefficient, Nusselt number and Sherwood number. It is observed that temperature is more subject to higher estimations of Brownian motion and thermophoresis diffusion while decays versus higher values of Prandtl number. Concentration field decays versus higher values of Schmidt number and enhances by increasing the values of activation energy parameter.

Absorption cooling systems – Review of various techniques for energy performance enhancement

Abstract: Absorption refrigeration technology was introduced to address some serious issues such as the energy crisis, increased fuel prices, and environmental problems associated with the conventional compression refrigeration systems. It has attracted an increasing deal of interest thanks to such advantages as utilization of low-grade heat sources and environment-friendly working fluid pairs. Nevertheless, this technology suffers from two major obstacles including the usually too large size of the cooling unit and the low coefficient of performance (COP), preventing the absorption systems from being commercially successful. Numerous research works have been done to develop strategies in order to improve the COP of the absorption systems, so as to make the absorption refrigeration technology more competitive with the conventional compression refrigeration systems. In this paper, it is intended to conduct a literature review on various technologies implemented to improve the COP of absorption refrigeration systems. Among effective and promising workarounds for increasing the COP of absorption refrigeration systems, this work refers to cycle design improvement, heat recovery method, development of new working pairs, adding sub-components, and improvement of operating conditions.

Grasping force prediction based on sEMG signals

Abstract: In order to realize the force control, when the prosthetic hand grasps the object, the forearm electromyography signal is collected by the multi-channel surface electromyography (sEMG) acquisition system. The grasping force information of the human hand is recorded by the six-dimensional force sensor. The root mean square (RMS) of the electromyography signal steady state is selected, which is an effective feature. The gene expression programming algorithm (GEP) and BP neural network are used to construct the prediction model and predict the grasping force. The force prediction accuracy of GEP algorithm and BP neural network algorithm are discussed under different grasping power levels and different grasping modes. The performance of the two algorithm models are evaluated by two measures of root mean square error (RMSE) and correlation coefficient (CC). The results show that the RMS eigenvalue extracted from the sEMG signal can better characterize the grasping force. The prediction model with GEP algorithm has smaller relative error and higher prediction effect.

On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators

Abstract: We investigate the existence of solutions for a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions. In this way, we use a generalization of the hybrid Dhage’s fixed point result for sum of three fractional operators. Finally, we give an example to illustrate our main result.

Can transfer function and Bode diagram be obtained from Sumudu transform

Abstract: In the last past year researchers have relied on the ability of Laplace transform to solve partial, ordinary linear equations with great success. Important analysis in signal analysis including the transfer function, Bode diagram, Nyquist plot and Nichols plot are obtained based on the Laplace transform. The output of the analysis depends only on the results obtained from Laplace transform. However, one weakness of Laplace transform is that the Laplace transform of even function is odd while the Laplace transform of an old function is even which is lack of conservation of properties. On the other hand there exist a similar integral transform known as Sumudu transform has the ability to conserve the properties of the function from real space to complex space. The question that arises in the work, is the following: Can we apply the Sumudu transform to construct new transfer functions that will lead to new Bode, Nichols and Nyquist plots? this question is answered in this work.

Transpiration effects on hybrid nanofluid flow and heat transfer over a stretching/shrinking sheet with uniform shear flow

Abstract: This paper considers the effect of transpiration on hybrid nanofluid flow and heat transfer over a stretching/shrinking sheet for uniform shear flow. The similarity equations are attained from the governing equations by using similarity transformation technique, and their solutions are obtained using the bvp4c solver in Matlab software. The effect of the several governing parameters on the flow and heat transfer characteristics are presented and interpreted theoretically. Results elucidate that dual solutions exist up to a certain range of the stretching/shrinking parameter. Moreover, the dual solutions are observed to occur for both stretching or shrinking cases in the present of suction parameter. An increasing of copper nanoparticle volume fractions generates an enhancement in the heat transfer coefficient, however dual behaviour is observed in the skin friction coefficient for the upper branch solutions. The temporal stability analysis is conducted to determine the stability of the dual solutions, and it is discovered that only one of them is stable and physically reliable.

New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method

Abstract: This article presents soliton solutions to a generalized nonlinear Fokas-Lenells equation via the Sine-Gordon expansion method. To uncover the clear picture of the gained solutions, the two and three-dimensional figures for the solutions are given. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations.

Dynamical characteristic of analytical fractional solitons for the space-time fractional Fokas-Lenells equation

Abstract: A new strategy exploiting together the modified Riemann–Liouville fractional derivative rule and two kinds of fractional dual-function methods with the Mittag–Leffler function is presented to solve fractional nonlinear models. As an example, the space-time fractional Fokas-Lenells equation is solved by this strategy, some new exact analytical solutions including bright soliton, dark soliton, combined soliton and periodic solutions are found. The comparison of two kinds of fractional dual-function methods is also presented. These solutions exist under a constraint among parameters of nonlinear dispersion, nonlinearity and self-steepening perturbation. In order to further study the optical soliton transport and better understand the physical phenomenon behind the model, dynamical characteristics of analytical fractional soliton solutions including some graphics and analysis is provided. The role of the fractional-order parameter is studied.

Flow and heat transfer of hybrid nanofluid over a permeable shrinking cylinder with Joule heating: A comparative analysis

Abstract: The objectives of the present study are (i) to observe the duality of solutions, and (ii) to investigate the flow and heat transfer of the hybrid nanofluid past a shrinking cylinder in the appearance of Joule heating. The single phase nanofluid model with modified thermophysical properties are used for the mathematical model. The similarity transformation simplifies the model (PDEs) into similarity (ordinary) differential equations. bvp4c solver is used to compute the reduced equations. For the validation part, the analytical solution is developed using an exact analytical method and compared with the numerical values for several cases. First and second solutions are observable for the shrinking cylinder case only if suction parameter is applied. Meanwhile, only the first solution is found to be stable from the stability analysis. The application of high suction strength make the reduced heat transfer rate is lower for hybrid nanofluid (Cu-Al2O3/water) than alumina-water nanofluid but, opposite result is found for the skin friction coefficient. The addition of curvature parameter (flat plate to cylinder) can quicken the separation process of boundary layer. This results are conclusive to the pair of alumina and copper only.

Numerical investigation and sensitivity analysis on bioconvective tangent hyperbolic nanofluid flow towards stretching surface by response surface methodology

Abstract: In a suspension of tangent hyperbolic bionanofluid keeping both nanoparticles and motile microorganisms, the thermobioconvective boundary layer flow was studied through an exponentially stretching surface utilizing response surface methodology (RSM). The constructed model of a tangent hyperbolic nanofluid in boundary layer flow is studied with implications of thermophoresis and Brownian motion. Condition of zero normal flux of nanomaterials is added at the surface to scatter the nanomaterials from the plate surface. The rate of heat transfer is analyzed using convective boundary condition. Numerical shooting strategy with Runge-Kutta scheme is to follow intently behind the similarity transformation to solve the system of governing equations. It is assumed that the output variables of interest are dependent on the governing input parameters. The sensitivity analysis is additionally introduced. It is discovered that the sensitivity of local Nusselt number increments by expanding Lewis and thermophoresis number while the highest non-dimensional Nusselt number appears close to the significant level for the thermophoresis and low level for the Brownian motion variable. Additionally, it is demonstrated that the average maximum mean thickness of motile microorganism appears at the highest level of Brownian motion and thermophoresis number and thermophoresis and Lewis numbers. The results would provide initial guidance for potential manufacture of devices.

On a nonlinear fractional order model of dengue fever disease under Caputo-Fabrizio derivative

Abstract: In this manuscript, we investigate epidemic model of dengue fever disease under Caputo and Fabrizio fractional derivative abbreviated as (CFFD). The respective investigation is devoted to qualitative theory of existence of solution for the model under consideration by using fixed point theory. After the establishing the qualitative aspect, we apply Laplace transform coupled with Adomian decomposition method to develop an algorithm for semi analytical solution under CFFD. In same line, we also develop the semi analytical solution for the considered model under usual Caputo fractional derivative (CFD). By using Matlab, we present both type of solutions via graphs and hence give some comparative remarks about the nature of the solutions of both derivatives.

Comparative study of the performance of air and geothermal sources of heat pumps cycle operating with various refrigerants and vapor injection

Abstract: Nowadays, due to the energy and environmental crisis, using renewable energy is considered to reduce environmental pollution. In this paper, a comprehensive review of geothermal source heat pumps (GSHPs) and air source heat pumps (ASHPs) are studied from various aspects including refrigerant change, single-stage heat pump and heat pump with an economizer. This study is conducted to meet the heating needs of the central laboratory of Hakim Sabzevari University. These cycles are analyzed using energy, exergy, and environmental and economic equations (4E analysis). The results show that the coefficient of performance (COP) and exergy efficiency values for the GSHP cycle are higher than the ASHP cycle, and the best refrigerant for both is R134A. The economic and environmental analysis also reveals that using the GSHP cycle can save the electricity to 239 MWh/year (by cycle equipment), which reduces CO2 emissions to 140 tons/year and saves costs 27,280 $/year, compared to ASHP. Moreover, by using an economizer in the heat pump cycle, the COP of the GSHP cycle improved by 9%. The exergy efficiency about 6.8% and the COP of the ASHP cycle grew about 7.5% and its exergy efficiency by 7.4%. It is concluded that the economizer has a more significant impact on the GSHP cycle.

New results on nonlocal functional integro-differential equations via Hilfer fractional derivative

Abstract: In this work, the existence of Hilfer fractional integro-differential equations with nonlocal conditions are discussed. To obtain such result, we use M o ¨ nch fixed point theorem and the techniques of noncompactness. An application is presented to validate the theoretical results.

An efficient numerical scheme for fractional model of HIV-1 infection of CD4+ T-cells with the effect of antiviral drug therapy

Abstract: In the present paper, a HIV - 1 infection of CD 4 + T-cells with the impact of drug treatment model of arbitrary order have been examined with the aid of Legendre wavelet operational matrix method. The technique employed to convert differential equations of arbitrary order into the linear or nonlinear algebraic equations, which are easy to handle by mathematical software. The comparison among the discussed methods with RK4, homotopy perturbation scheme, homotopy analysis approach, Laplace adomian-decomposition technique and Adam-Bashforth predictor-corrector scheme divulge that the present technique is authentic and valid for other engineering problems. It is noticed that the suggested scheme are more efficient and effective.

Cu-Al2O3/water hybrid nanofluid flow over a permeable moving surface in presence of hydromagnetic and suction effects

Abstract: In this new era of technology in fluid field, hybrid nanofluid has become a fruitful interest topic among researchers due to it thermal properties and potential which gives better result compared to nanofluid in enhancing the heat transfer rate. The intention here is to present the significant effects of suction and magnetic field over a moving plate containing hybrid nanofluid with base fluid is water, Alumina Oxide (Al2O3) and Copper (Cu) as the nanoparticles. A mathematical modelling consists of partial differential equation for the fluid flow are constructed and transformed to a set of ordinary differential equations hence solved numerically using bvp4c in MATLAB. Effects of magnetohydrodynamics (MHD), M, suction, S and relevant thermophysical properties on velocity, temperature, skin friction, C f and local Nusselt, N u x number are thoroughly examined and presented graphically. It is noted that duality exists in certain range when λ c - 1 and unique solution at λ > - 1 . The range on duality of solution are widen as the values of M and S increase. Due to that, a stability analysis is implied to determine which duality of solution is stable and realizable. As M and ϕ 2 increase, the skin friction increases. For rate of heat transfer, as M increase, the heat transfer rate increase while for arising of ϕ 2 , the heat transfer decrease. Furthermore, it is noted that the hybrid nanofluid possess better result compared to nanofluid.

Dynamical analysis of the nonlinear complex fractional emerging telecommunication model with higher–order dispersive cubic–quintic

Abstract: In this paper, a nonlinear fractional emerging telecommunication model with higher–order dispersive cubic–quintic is studied by using two recent computational schemes. This kind of model is arising in many applications such as machine learning and deep learning, cloud computing, data science, dense sensor network, artificial intelligence convergence, integration of Internet of Things, self–service IT for business users, self-powered data centers, and dense sensor networks (DSNs) that is used in the turbine blades monitoring and health monitoring. Two practical algorithms (modified Khater method and sech–tanh functions method) are applied to higher–order dispersive cubic–quintic nonlinear complex fractional Schrodinger ( NLCFS ) equation. Many novel traveling wave solutions are constructed that do not exist earlier. These solutions are considered as the icon key in the emerging telecommunication field, were they able to explain the physical nature of the waves spread, especially in the dispersive medium. For more illustration, some attractive sketches are also depicted for the interpretation physically of the achieved solutions.

Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system

Abstract: Robust modeling of a multimodal dynamic system is a challenging and fast-growing area of research In this study, an integrated bi-modal computing paradigm based on Nonlinear Autoregressive Radial Basis Functions (NAR-RBFs) neural network model, a new family of deep learning with the strength of hybrid artificial neural network, is presented for the solution of nonlinear chaotic dusty system (NCDS) of tiny ionized gas particles arising in fusion devices, industry, astronomy, and space In the proposed methodology, special transformations are introduced for a class of differential equations, which convert the local optimum to a global optimum The proposed NAR-RBFs neural network model is implemented on bi-model NCDS represented with Van der Pol-Methiew Equation (VdP-ME) for different scenarios based on variation in dust gain production and loss for both small and large time domains Excellent agreement for proposed bimodal computing paradigm by the result with the standard state of the arts numerical solvers is verified by attaining RMSE up to 1E−38 for the nonlinear VDP-ME Accuracy of the proposed model in the critical time domain is also validated by convergence, stability and consistency analysis on statistics calculated from absolute error, root-mean-square error, and analysis of variance metrics

Boiling heat transfer characteristics of graphene oxide nanoplatelets nano-suspensions of water-perfluorohexane (C6F14) and water-n-pentane

Abstract: In the present work, the boiling heat transfer coefficient (BHTC) and fluid flow characteristics of graphene oxide nanoplatelets (GONPs) nano-suspensions in an annular heat exchanger (AHEX) were experimentally investigated. The BHTC, pressure drop (PD) and the friction factor (FF) of the heat exchanger was quantified, and effects of various operating conditions including heat flux (HF), flow rate (FR), the temperature of the nano-suspension and the mass concentration (MC) of the GONPs on the HTC and the PD of the system was assessed. Results showed that by increasing the HF, the weight concentration of the GONPs, and the temperature of the working fluid, the BHTC of the system increases. Also, the presence of GONPs can augment the friction forces, viscosity, and, as a result, increase the PD and the FF of the system. For all the experiments, the BHTC of the system was more significant than water. A comparison between water-perfluorohexane and water- n-pentane nano-emulsions revealed that water-n pentane has better thermal performance and lower PD in comparison with perfluorohexane despite the presence of the GONPs within the bulk of the nano-emulsion.

A study of changes in temperature profile of porous fin model using cuckoo search algorithm

Abstract: For analysis of physical properties of different materials, rectangular porous fins are used to examine the heat transformation through a system. In this paper, a metaheuristic is combined with neural computing modelling to study the effects of temperature changes in a porous fin model. Cuckoo search algorithm is used as an efficient optimization technique to find the best weights to reduce the mean squared error in the required temperature profile. The governing partial differential equation is converted into a non-linear ordinary differential equation subject to certain boundary conditions. Two individual cases, of silicon nitride ( Si 3 N 4 ) and Aluminium (Al), are considered. In the proposed procedure, the Cuckoo Search(CS) algorithm is combined with the artificial neural network (ANN), namely CS-ANN, to solve the differential equations and obtain solutions with better accuracy.

Jaya optimization algorithm for transient response and stability enhancement of a fractional-order PID based automatic voltage regulator system

Abstract: Considering the higher flexibility in tuning process and finer control action of the fractional-order proportional integral derivative (FOPID) controller over the conventional proportional integral derivative (PID) controller, this paper explores its application in the automatic voltage regulator system. FOPID contains five tuning parameters as compared to three in the conventional PID controller. The additional tuning knobs in FOPID provide increased control flexibility and precise control action, however, their inclusion makes the tuning process more complex and tedious. Thus, the intelligence of an artificial intelligence (AI) technique called jaya optimization algorithm (JOA) is utilized in order to obtain an optimal combination of FOPID gains which further led to the optimal transient response and improved stability of the considered AVR system. To validate the performance superiority of the proposed approach its corresponding system’s dynamic response is compared with that of the other well-known AI-based approaches explored in recent literature. Furthermore, the stability study of the proposed AVR system is carried out by evaluating its pole/zero and bode maps. Finally, the robustness of the proposed optimized AVR system against the system’s parameter variation is evaluated by varying the time constants of all the four components of AVR (generator, exciter, amplifier and sensor) from −50% to +50% independently. The proposed algorithm based FOPID tuning technique provides 59.82%, 56.09%, 14.94%, 34.24%, 35.70%, 21.64%, 12.0%, 41.33%, 14.84% and 15.17% reduced overshoot than that of differential evolution (DE), particle swarm optimization (PSO), Artificial Bee Colony (ABC), Bibliography Based Optimization (BBO), Grasshopper Optimization Algorithm (GOA), Pattern Search Algorithm (PSA), Improved Kidney Inspired Algorithm (IKA), Whale Optimization Algorithm (WOA), Salp Swarm Algorithm (SSA) and Local Unimodal Sampling (LUS) algorithm respectively, thus validates its competence and effectiveness.

Analytical approach for time fractional wave equations in the sense of Yang-Abdel-Aty-Cattani via the homotopy perturbation transform method

Abstract: Very recently, Yang, Abdel-Aty and Cattani (2019) introduced a new and intersting fractional derivative operator with non-singular kernel involving Rabotnov fractional-exponential function. In this paper, we present a general framework of the homotopy perturbation transform method (HPTM) for analytic treatment of time fractional partial differential equations in the sense of Yang-Abdel-Aty-Cattani. As applications, time fractional wave equations involving Yang-Abdel-Aty-Cattani fractional derivatives are solved. The solutions are obtained in the form of series involving Prabhakar functions.

Stability and numerical simulation of a fractional order plant-nectar-pollinator model

Abstract: In this article, a plant-nectar-pollinator (PNP) model has been generalized involving Atangana-Baleanu fractional-order derivative. This new kind of derivative provide us important information of variables specially used in the complex system. Existence and uniqueness (EU) of solutions for the fractional order PNP model are examined via Picard-Lindelof method and stability analysis is discussed by Picard’s stability technique. The results show better performance of the model under fractional derivative proving that the dynamics of the PNP can be well understood if non-local effects are considered within the model. Moreover, the developed model is illustrated with numerical examples for different orders of the model.

Novel fixed point approach to Atangana-Baleanu fractional and Lp-Fredholm integral equations

Abstract: In this article, we introduce an extended F -metric and proved related fixed point results. Subsequently, we mainly focus on (a): Solution for the Atangana-Baleanu fractional integral of order ∝ of a function f ( t ) I t ∝ s AB ζ ( t ) = 1 - ∝ B ( ∝ ) ζ ( t ) + ∝ B ( ∝ ) Γ ( ∝ ) ∫ 0 t ζ ( ρ ) ( t - ρ ) ∝ - 1 d ρ ; where 0 ∝ ⩽ 1 , 0 t s and it is worthy to mention B ( 0 ) and B ( 1 ) are equal to 1. (b): L P type solution ( 1 p ∞ ) for the linear Fredholm integral equation of the second kind where

A new model of fractional Casson fluid based on generalized Fick’s and Fourier’s laws together with heat and mass transfer

Abstract: A new technique for modelling the fractional model of Casson fluid is used. More exactly, the Caputo fractional model has been developed using the generalized Fick’s and Fourier’s laws. The magnetohydrodynamics free convection flow of Casson fluid in a channel has been considered. A new transformation is applied to the energy and mass equations and then solved by using the Laplace and Fourier sine transformations jointly. The final solutions are presented in terms of special function, namely, the Mittag-Leffler function. The effects of various physical parameters have been portrayed in graphs and tables and discussed.