Solutions of Some Linear Fractional Partial Differential Equations in Mathematical Physics

Abstract

In this article, we use double Laplace transform method to find solution of general linear fractional partial differential equation in terms of Mittag-Leffler function subject to the initial and boundary conditions. The efficiency of the method is illustrated by considering fractional wave and diffusion equations, Klein-Gordon equation, Burger’s equation, Fokker-Planck equation, KdV equation, and KdV-Burger’s equation of mathematical physics.

Numerical Solution of a Class of Nonlinear Partial Differential Equations by Using Barycentric Interpolation Collocation Method

“…The relations between the components , of the formula (8) The function values of formula (6) and formula (7) at the node form column vectors , ( , ) , and they are as follows:…”

“…We also consider the application of a domain-type method of fundamental solutions together with a Picard iteration scheme for solving nonlinear elliptic PDEs [6] and a deep learning-based approach that can handle general high-dimensional parabolic PDEs [7]. Couple double Laplace transform with iterative method solves nonlinear Klein-Gordon equation subject to initial and boundary conditions [8]. The variational iteration method (VIM) and homotopy perturbation method (HPM) are used for various kinds of nonlinear problems ( [9][10][11][12]).…”

Remarks on Analytical Solutions of a Non-Homogeneous Gas Dynamic Model via Successive Approximation Method

“…The analytic approaches for these problems are frequently limited and difficult to evaluate. Numerical approaches have been judged more efficient and reliable in solving the gas dynamic models (equations) and other differential models in this regard [22][23][24][25][26][27][28][29][30][31].…”

SAM approximate solutions of some evolution equations

“…For a better understanding of evolution equations, in terms of derivations and formats, readers are referred to [1,3]. Different solution experts have recently discussed numerous methods for finding an exact or numerical solution to ordinary or partial differential models [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. In this work, a novel approach termed Successive Approximation Method (SAM) is applied to some non-linear evolution models.…”