Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

H. M. Srivastava,Jie Li,Xiao-Jun Yang,Gong-Nan Xie,Ai-Min Yang

doi:10.1155/2014/365981

Abstract

The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

Highlights

Fractional calculus [1] has successfully been used to study the mathematical and physical problems arising in science and engineering
The properties for local fractional Laplace transform used in the paper are given as [12]
We introduce the idea of local fractional variational iteration method [16, 17], which is coupled by the local fractional variational iteration method and Laplace transform

Summary

Introduction

Fractional calculus [1] has successfully been used to study the mathematical and physical problems arising in science and engineering. Some methods for solving the local fractional differential equations were suggested, such as the Cantor-type cylindricalcoordinate method [15], the local fractional variational iteration method [16, 17], the local fractional decomposition method [18], the local fractional series expansion method [19], the local fractional Laplace transform method [20], and local fractional function decomposition method [21, 22]. The coupling schemes for local fractional variational iteration method and Laplace transform were suggested in [23]. Our aim is to use the local fractional Laplace variational iteration method to solve the linear local fractional partial differential equations.

Local Fractional Calculus and Local Fractional Laplace Transform

Analysis of the Method

Conclusions