Numerical Double Sumudu Transform for Nonlinear Mixed Fractional Partial Differential Equations

Abstract

In this paper, we are going to study a nonlinear fractional partial differential equations by double Sumudu transformation coupled with Adomian decomposition method or with variational iteration method. For this case, we choose an important fractional partial differential equations, such as parabolic-hyperbolic with mixed fractional derivatives (homogeneous and nonhomogeneous) types. Some examples are given here to illustrate efficiency of this method.

A Note on the Application of the Double Sumudu–Generalized Laplace Decomposition Method and 1+1- and 2+1-Dimensional Time-Fractional Boussinesq Equations

“…A new generalized Laplace transform was studied in [18], and some properties of this transform are introduced in [19], while some ideas related to generalized Laplace transforms were employed to find the solutions of partial differential equations (PDEs) [20]. The double Sumudu transformation method was utilized in several papers (see [21][22][23]). Recently, the authors of [24,25] used Sumudu-generalized Laplace transform decomposition to solve fractional third-order dispersive partial differential equations and the 2+1-Pseudoparabolic Equation.…”

A Note on the Time-Fractional Navier–Stokes Equation and the Double Sumudu-Generalized Laplace Transform Decomposition Method

“…In the paper [13], the authors discussed the convergence properties of double Sumudu transformation and applied it to obtain the exact solution of the Volterra integro-partial differential equation. The double Sumudu transform is connected with the Adomian decomposition method to obtain the analytical solution of nonlinear fractional partial differential equations [14].…”