A new iterative algorithm on the time-fractional Fisher equation: Residual power series method

Maysaa’ Mohamed Al Qurashi,Dumitru Baleanu,Zeliha Korpinar,Mustafa Inc

doi:10.1177/1687814017716009

Abstract

In this article, the residual power series method is used to solve time-fractional Fisher equation. The residual power series method gets Maclaurin expansion of the solution. The solutions of prese...

Highlights

Important care has been assigned to the work of the fractional calculus during the last few decades and its numerous utilizations in the physics, regular variation in biophysics, thermodynamics, blood flow phenomena, viscoelasticity, electrical circuits, aerodynamics, astrophysics, biology, control theory, and so on.[1,2,3,4]
This is the fundamental advantage of fractional differential equations in return usual integer order problems
In the work by Yang et al.,[5] researchers applied the local fractional derivative operator for obtaining the non-differential solution for diffusion equation in fractal heat transfer; in the work by Gao et al.,[6] the exact solution for the local fractional diffusion equation in fractal one-dimensional space is obtained; in the work by Yang et al.,[7] the analytical solutions of the sub-diffusion and wave equations are obtained by utilizing the local fractional variational iteration method; in the work by Gao and Yang,[8] the local fractional Euler’s method is applied to obtain numerical solution for the local fractional heatrelaxation equation; in the work by Yang et al.,[9] authors analyzed the exact traveling wave solutions for local fractional Korteweg–de Vries (KdV) equation; in

Summary

Introduction

Important care has been assigned to the work of the fractional calculus during the last few decades and its numerous utilizations in the physics, regular variation in biophysics, thermodynamics, blood flow phenomena, viscoelasticity, electrical circuits, aerodynamics, astrophysics, biology, control theory, and so on.[1,2,3,4] fractional derivatives supply an important implement for the definition of recollection and hereditary characteristics of different necessaries and treatment. Keywords Residual power series method, time-fractional Fisher equation, series solution The base purpose of our work is to present practice of RPSM in the touch of the Caputo fractional differential to examine and establish an approximate solution of the space-time-fractional order Fisher equation[23]

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Results

Conclusion