Showing papers by "Doddabhadrappla Gowda Prakasha published in 2020"

A new study of unreported cases of 2019-nCOV epidemic outbreaks

Abstract: 2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q-homotopy analysis transform method (q-HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.

Novel dynamic structures of 2019-ncov with nonlocal operator via powerful computational technique

Abstract: In this study, we investigate the infection system of the novel coronavirus (2019-nCoV) with a nonlocal operator defined in the Caputo sense. With the help of the fractional natural decomposition method (FNDM), which is based on the Adomian decomposition and natural transform methods, numerical results were obtained to better understand the dynamical structures of the physical behavior of 2019-nCoV. Such behaviors observe the general properties of the mathematical model of 2019-nCoV. This mathematical model is composed of data reported from the city of Wuhan, China.

New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function

Abstract: In this paper, numerical solution of the mathematical model describing the deathly disease in pregnant women with fractional order is investigated with the help of q-homotopy analysis transform method (q-HATM). This sophisticated and important model is consisted of a system of four equations, which illustrate a deathly disease spreading pregnant women called Lassa hemorrhagic fever disease. The fixed point theorem is considered so as to demonstrate the existence and uniqueness of the obtained numerical solution for the governing fractional model. The proposed method is also included the Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. In order to illustrate and validate the efficiency of the future technique, the projected model in the sense of fractional order is also considered. Moreover, the physical behaviors of the obtained numerical results are presented in terms of simulations for diverse fractional order.

New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach

Abstract: This manuscript investigates the fractional Phi-four equation by using q -homotopy analysis transform method ( q -HATM) numerically. The Phi-four equation is obtained from one of the special cases of the Klein-Gordon model. Moreover, it is used to model the kink and anti-kink solitary wave interactions arising in nuclear particle physics and biological structures for the last several decades. The proposed technique is composed of Laplace transform and q -homotopy analysis techniques, and fractional derivative defined in the sense of Caputo. For the governing fractional-order model, the Banach’s fixed point hypothesis is studied to establish the existence and uniqueness of the achieved solution. To illustrate and validate the effectiveness of the projected algorithm, we analyze the considered model in terms of arbitrary order with two distinct cases and also introduce corresponding numerical simulation. Moreover, the physical behaviors of the obtained solutions with respect to fractional-order are presented via various simulations.

Regarding new numerical solution of fractional Schistosomiasis disease arising in biological phenomena

Abstract: In this paper, we study to find the numerical solution of fractional Schistosomiasis disease by using a numerical method. Fractional Schistosomiasis disease model is used to symbolize a parasitic disease caused by trematode flukes of the genus Schistosoma. The physical behaviour of results obtained by using q-homotopy analyses transform method (q-HATM) in terms of plots for different fractional-order is captured. The results obtained by using considered method is more effective and easy to apply in order to examine the nature of multi-dimensional differential equations of fractional order arising in biological disease.

An Efficient Computational Technique for Fractional Model of Generalized Hirota–Satsuma-Coupled Korteweg–de Vries and Coupled Modified Korteweg–de Vries Equations

Abstract: The aim of the present investigation to find the solution for fractional generalized Hirota–Satsuma coupled Korteweg–de-Vries (KdV) and coupled modified KdV (mKdV) equations with the aid of an efficient computational scheme, namely, fractional natural decomposition method (FNDM). The considered fractional models play an important role in studying the propagation of shallow-water waves. Two distinct initial conditions are choosing for each equation to validate and demonstrate the effectiveness of the suggested technique. The simulation in terms of numeric has been demonstrated to assure the proficiency and reliability of the future method. Further, the nature of the solution is captured for different value of the fractional order. The comparison study has been performed to verify the accuracy of the future algorithm. The achieved results illuminate that, the suggested computational method is very effective to investigate the considered fractional-order model.

Solution for fractional generalized Zakharov equations with Mittag-Leffler function

Abstract: The pivotal aim of the present work is to find the solution for fractional generalized Zakharov (FGZ) equations using q -homotopy analysis transform method ( q -HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q -homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the proposed technique, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The obtained results elucidate that, the considered algorithm is easy to implement, highly methodical as well as accurate and very effective to analyse the behaviour of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

Solution for fractional forced KdV equation using fractional natural decomposition method

Abstract: The fractional natural decomposition method (FNDM) is employed in the present investigation to find the solution for fractional forced Korteweg-de Vries (FF-KdV) equation. Three distinct cases are chosen for each equation to validate and illustrate the effectiveness of the future technique. The behaviour for different values of Froude number (Fr) has been presented to assure the proficiency and reliability and of the considered method. Moreover, we captured the behaviour of the FNDM solution for distinct arbitrary order. The obtained results elucidate that, the considered method is very effective and easy to employ while analyse the behaviour of nonlinear fractional differential equations arising in connected areas of science and technology.

Iterative method applied to the fractional nonlinear systems arising in thermoelasticity with mittag-leffler kernel

Abstract: In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is ...

An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

Abstract: Correspondence D. G. Prakasha, Department of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere 577002, India. Email: prakashadg@gmail.com In this paper, the q-homotopy analysis transform method (q-HATM) is applied to find the solution for the fractional Lakshmanan-Porsezian-Daniel (LPD) model. The LPD model is the generalization of the non-linear Schrödinger (NLS) equation. The proposed method is graceful fusions of Laplace transform technique with q-homotopy analysis scheme, and the derivative is considered in Caputo sense. In order to validate and illustrate the efficiency of the proposed method, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured for the three different cases in terms of 3D and contour plots for diverse values of the fractional order. The obtained results confirm that the future method is easy to implement, highly methodical, and very effective to analyse the behaviour of complex non-linear fractional differential equations exist in the connected areas of science and engineering.

Analytical approach for fractional extended Fisher–Kolmogorov equation with Mittag-Leffler kernel

Abstract: A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed with Atangana–Baleanu (AB) operator, and the technique we consider is a mixture of the q-homotopy analysis scheme and the Laplace transform. The fixed point hypothesis is considered for the existence and uniqueness of the obtained solution of this model. For the validation and effectiveness of the projected scheme, we analyse the FEFK equation in terms of arbitrary order for the two distinct cases. Moreover, numerical simulation is demonstrated, and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.

An efficient technique for two-dimensional fractional order biological population model

Abstract: In this paper, we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method (FNDM). The proposed method is a graceful ...

A novel approach for nonlinear equations occurs in ion acoustic waves in plasma with Mittag-Leffler law

Abstract: The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM).,The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator.,The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order.,To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

A reliable analytical technique for fractional Caudrey-Dodd-Gibbon equation with Mittag-Leffler kernel

Abstract: Abstract The pivotal aim of the present work is to find the solution for fractional Caudrey-Dodd-Gibbon (CDG) equation using q-homotopy analysis transform method (q-HATM). The considered technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the projected fractional-order model. In order to illustrate and validate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of q-HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The obtained results elucidate that, the considered algorithm is easy to implement, highly methodical as well as accurate and very effective to examine the nature of nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

Fractional SIR Epidemic Model of Childhood Disease with Mittag-Leffler Memory

Abstract: The susceptible-infected-recovered (SIR) epidemic model of childhood disease is analysed in this chapter with the Atanagana-Baleanu (AB) fractional operator The considered non-linear model has been efficiently applied to describe the evolution of childhood disease in a population and its influence on the community The Adams-Bashforth scheme is applied to find and analyse the solution for the proposed model The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the derived solution for the future fractional-order model Two distinct explanatory cases are considered and for both cases, the simulations have been demonstrated in terms of plots The present investigation illuminates that the AB derivative plays a vital role in the analysis and describes the behaviour of the diverse model arising in human disease

The ℳ-projective curvature tensor field on generalized (κ,μ)-paracontact metric manifolds

Abstract: Abstract We consider generalized ( κ , μ ) {(\\kappa,\\mu)} -paracontact metric manifolds satisfying certain flatness conditions on the ℳ {\\mathcal{M}} -projective curvature tensor. Specifically, we study ξ- ℳ {\\mathcal{M}} -projectively flat and ℳ {\\mathcal{M}} -projectively flat generalized ( κ , μ ) {(\\kappa,\\mu)} -paracontact metric manifolds and, further, ϕ- ℳ {\\mathcal{M}} -projectively symmetric generalized ( κ ≠ - 1 , μ ) {(\\kappa\ eq-1,\\mu)} -paracontact metric manifolds. We prove that they are characterized by certain structures whose properties are discussed in some detail.

Evolution and analysis of COVID-2019 through a fractional mathematical model

Abstract: Throughout the globe, mankind is in vastly infected situations due to a cruel and destructive virus called coronavirus (COVID-19). The pivotal aim of the present investigation is to analyze and examine the evolution of COVID-19 in India with the available data in two cases first from the beginning to 31st March and beginning to 23rd April in order to show its exponential growth in the crucial period. The present situation in India with respect to confirmed, active, recovered and deaths cases have been illustrated with the aid of available data. The species of novel virus and its stages of growth with respect some essential points are presented. The exponential growth of projected virus by the day-to-day base is captured in 2D plots to predict its developments and identify the needs to control its spread on mankind. Moreover, the SEIR model is considered to present some interesting consequences about COVID-19 within the frame of fractional calculus. A newly proposed technique called q-Homotopy analysis transform method (q-HATM) is hired to find the solution for the nonlinear system portraying projected model and also presented the existence and uniqueness of the obtained results with help of fixed point theory. The behaviour has been captured with respect to fractional order and time.