Analytical Solutions to Investigate Fractional Newell-Whitehead Nonlinear Equation Using Sumudu Transform Decomposition Method

Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform

and Applied Analysis 3 4. Solution by Homotopy Perturbation Sumudu Transform Method (HPSTM) 4.1. Basic Idea of HPSTM. To illustrate the basic idea of this method, we consider a general fractional nonlinear nonhomogeneous partial differential equationwith the initial condition of the form D α t U (x, t) + RU (x, t) + NU (x, t) = g (x, t) , (11) U (x, 0) = f (x) , (12) where Dα t U(x, t) is the C...

Analytical solutions for the fractional Fisher's equation

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

On Sumudu Transform Method in Discrete Fractional Calculus

and Applied Analysis 3 2. Preliminaries on Time Scales A time scale T is an arbitrary nonempty closed subset of the real numbers R. The most wellknown examples are T R, T Z, and T q : {qn : n ∈ Z}⋃{0}, where q > 1. The forward and backward jump operators are defined by σ t : inf{s ∈ T : s > t}, ρ t : sup{s ∈ T : s < t}, 2.1 respectively, where inf ∅ : supT and sup ∅ : inf T. A point t ∈ T is sa...

A new Sumudu transform iterative method for time-fractional Cauchy reaction–diffusion equation

In this paper, a new Sumudu transform iterative method is established and successfully applied to find the approximate analytical solutions for time-fractional Cauchy reaction-diffusion equations. The approach is easy to implement and understand. The numerical results show that the proposed method is very simple and efficient.