Solving Poisson Equation within Local Fractional Derivative Operators

Hassan Kamil Jassim

doi:10.11131/2017/101253

Abstract

In this paper, we are concerned with finding approximate solutions to local fractional Poisson equation by using the reduced differential transform method (RDTM) and homotopy perturbation transform method (HPTM). The presented methods are considered in the local fractional operator sense. Illustrative examples for handling the local fractional Poisson equation are given. The obtained results are given to show the sample and efficient features of the presented techniques to implement partial differential equations with local fractional derivative operators.

Highlights

Editor Wen-Xiu MaDates Received 7 November 2016 Accepted 28 July 2017The Poisson equation plays an important role in mathematical physics [1, 2]; that is, it describes the electrodynamics and intersecting interface [3, 4]
From equations (3.6) and (3.10), approximate solution of the given problem equation (3.1) by using local fractional homotopy perturbation transform method (HPTM) is the same results as that obtained by the local fractional reduced differential transform method (RDTM) and the local fractional variational iteration method [6]
The local fractional RDTM and the local fractional HPTM provide the solutions in terms of convergent series with computable components

Summary

Introduction

The Poisson equation plays an important role in mathematical physics [1, 2]; that is, it describes the electrodynamics and intersecting interface [3, 4]. The Poisson equation (PE) with local fractional derivative operators (LFDOs) was presented in [6] as follows:. A many of approximate and analytical methods have been utilized to solve the ordinary and partial differential equations with local fractional derivative operators such as local fractional Adomian decomposition method [7,8,9,10,11], local fractional variational iteration method [6, 7, 12,13,14,15], local fractional function decomposition method [8, 16], local fractional. How to cite this article: Hassan Kamil Jassim, “Solving Poisson Equation within Local Fractional Derivative Operators,” Research in Applied Mathematics, vol 1, Article ID 101253, 12 pages, 2017.

Local Fractional HPTM

Two Illustrative Examples

Conclusions