Implementation and Convergence Analysis of Homotopy Perturbation Coupled With Sumudu Transform to Construct Solutions of Local-Fractional PDEs

A New Technique of Reduce Differential Transform Method to Solve Local Fractional PDEs in Mathematical Physics

In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising inmathematical physics with local fractional derivative operators (LFDOs). To get approximate solutionsof these equations, we utilize the reduce differential transform method (RDTM) which is basedupon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. Theobtained ...

Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations

In this paper, we propose a combined form of the sumudu transform method with the homotopy perturbation method to solve nonlinear equations. This method is called the homotopy perturbation sumudu transform method (HPSTM). The nonlinear terms can be easily handled by the use of He’s polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoi...

Series Solutions of Time-Fractional PDEs by Homotopy Analysis Method

The homotopy analysis method HAM is applied to solve linear and nonlinear fractional partial differential equations fPDEs . The fractional derivatives are described by Caputo’s sense. Series solutions of the fPDEs are obtained. A convergence theorem for the series solution is also given. The test examples, which include a variable coefficient, inhomogeneous and hyperbolic-type equations, demons...

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...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations