Sumudu Transform Method For Solving Fractional Differential Equations And Fractional Diffusion-wave Equation

Abstract

In this paper, we obtain the solutions of a cauchy problems for differential equations with the Caputo fractional derivative and the solution of fractional Diffusion-Wave equation by using Sumudu transform techniques. The results presented here are in compact and elegant expressed in term of Mittag-Leffler function and generalized Mittag-Leffler function which are suitable for numerical computation.

Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method

“…Many researchers have proposed various methods to solve the time-fractional diffusion-wave equations from the perspective of analytical solution and numerical solution. The method of separation of variables in [1], Sumudu transform method in [2], and decomposition method in [3] were used to construct analytical approximate solutions of fractional diffusion-wave equations, respectively. Finite difference schemes in [4][5][6][7] were widely used to solve the numerical solutions of the fractional diffusion-wave equations.…”

Two-dimensional Bernoulli wavelets with satisfier function in the Ritz–Galerkin method for the time fractional diffusion-wave equation with damping

“…In the case q ¼ 2, this equation is named telegraph equation. Recently, considerable amount of papers have been proposed methods for solving the FDWE [2][3][4][5][6][7][8][9][10][11][12][13]. Chen et al [1] obtained the analytical solution by the method of separation of variables and proposed the numerical solution with finite difference method.…”

“…In [10], Hu and Zhang used finitedifference methods for fourth-order fractional diffusionwave. Sumudu transform method for solving fractional differential equations and fractional diffusion-wave equation applied by Darzi et al [11]. Hosseini et al [12] employed the meshless local radial point interpolation method which is based on the Galerkin weak form and radial point interpolation approximation for solving FDWE.…”

Wavelets method for the time fractional diffusion-wave equation

“…For more details about some important properties of the fractional diffusion equation and diffusion wave equation, the interested reader is advised to see [13][14][15]. In the last few years, several numerical methods have been proposed for solving FDWE, for instance see [12,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. In recent years, the LWs have been applied for solving some fractional differential equations, for instance see [31][32][33].…”