Fractional Differential Equations

In this research, we aim to propose a new fractional model for human liver involving Caputo–Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard–Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives.

A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative

Combined impact of Cattaneo-Christov double diffusion and radiative heat flux on bio-convective flow of Maxwell liquid configured by a stretched nano-material surface

Integral formulas in Riemannian geometry

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.

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

In present work, we investigate the numerical solution of time-fractional Jaulent–Miodek (JM) equations with the aid of two novel techniques namely, coupled fractional reduced differential transfor...

Numerical simulation for fractional Jaulent–Miodek equation associated with energy-dependent Schrödinger potential using two novel techniques

The present paper aims at studying a Ricci solitons on para-Sasakian manifolds. We give the results on Ricci solitons in para-Sasakian manifold satisfying the conditions 0 = ) , ( R X S   , 0 = ) , ( P X R   and 0 = ) , ( H X R   ,where P , H are pseudo-projective and quasi-conharmonic curvature tensors, respectively. MSC(2000): 53C21; 53C44; 53C25.

/pdf/ricci-solitons-on-para-sasakian-manifolds-17li1w4rx5.pdf

Ricci Solitons on Para-Sasakian Manifolds

In the present investigation, the q-homotopy analysis transform method (q-HATM) is applied to find approximated analytical solution for the system of fractional differential equations describing the unsteady flow of a polytropic gas. Numerical simulation has been conducted to prove that the proposed technique is reliable and accurate, and the outcomes are revealed using plots and tables. The comparison between the obtained solutions and the exact solutions shows that the proposed method is efficient and effective in solving nonlinear complex problems. Moreover, the proposed algorithm controls and manipulates the obtained series solution in a huge acceptable region in an extreme manner and it provides us a simple procedure to control and adjust the convergence region of the series solution.

An efficient technique for a fractional-order system of equations describing the unsteady flow of a polytropic gas

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

\n In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation 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 Mittag–Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.

Doddabhadrappla Gowda Prakasha

Papers

Numerical simulation for fractional Jaulent–Miodek equation associated with energy-dependent Schrödinger potential using two novel techniques

Ricci Solitons on Para-Sasakian Manifolds

An efficient technique for a fractional-order system of equations describing the unsteady flow of a polytropic gas

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

An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag–Leffler Kernel