On the solutions of electrohydrodynamic flow with fractional differential equations by reproducing kernel method

Abstract

Abstract:In this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM) is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.

Study of Magnetohydrodynamic Pulsatile Blood Flow through an Inclined Porous Cylindrical Tube with Generalized Time-Nonlocal Shear Stress

“…Sheng et al [42] reported that the numerical inverse Laplace transform algorithms are efficacious and reliable for fractional-order differential equations. Stehfest's algorithm [31] successfully used by Tong et al [43] and Jiang et al [44]. Therefore, in this work, we apply the numerical algorithm of the inverse Laplace transform method to Eq.…”

“…Many students are interested in using fractional dynamics to solve problems in classical dynamics. However, Riemann-Liouville and Caputo fractional derivatives are commonly used, and this generalization can be done by using different other fractional approaches/definitions [31,32].…”

Further fresh and general traveling wave solutions to some fractional order nonlinear evolution equations in mathematical physics

“…Therefore, it has become the core aim in the research area of fractional related problems that how to develop a stable approach for investigating the solutions to FNLEEs in analytical or numerical form. Many researchers have offered different approaches to construct analytic and numerical solutions to FNLEEs as well as integer order and put them forward for searching traveling wave solutions, such as the He-Laplace method [10], the exponential decay law [11], the reproducing kernel method [12], the Jacobi elliptic function method [13], the À G 0 =G Á -expansion method and its various modifications [14][15][16][17][18], the exp-function method [19], the sub-equation method [20,21], the first integral method [22], the functional variable method [23], the modified trial equation method [24], the simplest equation method [25], the Lie group analysis method [26], the fractional characteristic method [27], the auxiliary equation method [28,29], the finite element method [30], the differential transform method [31], the Adomian decomposition method [32,33], the variational iteration method [34], the finite difference method [35], the homotopy perturbation method [36] and the He's variational principle [37], the new extended direct algebraic method [38,39], the Jacobi elliptic function expansion method [40], the conformable double Laplace transform [41] etc. But each method does not bear high acceptance for the lacking of productivity to construct the closed form solutions to all kind of FNLEEs.…”

Daftar-Gejii-Jafaris method for linear and nonlinear third order fractional differential equation

“…Fractional partial differential equations have gained considerable importance recently in the literature. These equations have significant applications in finance, applied sciences, seismology engineering, physics and biology [1,18,19,21,23,32]. Fractional differential equations can be solved separately depending on time and space variables.…”