Abstract
In this paper, the time-fractional Fisher’s equation (TFFE) is considered to exam the analytical solution using the Laplace q-Homotopy analysis method (Lq-HAM)â€. The Lq-HAM is a combined form of q-homotopy analysis method (q-HAM) and Laplace transform. The aim of utilizing the Laplace transform is to outdo the shortage that is mainly caused by unfulfilled conditions in the other analytical methods. The results show that the analytical solution converges very rapidly to the exact solution.
Highlights
Fractional differential equations (FDEs) represent an important area of study because of their applications in various fields of science and engineering
We introduce the basic idea of Laplace q-Homotopy analysis method (Lq-HAM) for time-fractional Fisher’s equation (TFFE)
We apply the Lq-HAM for two examples
Summary
Fractional differential equations (FDEs) represent an important area of study because of their applications in various fields of science and engineering. Is a real parameter, represents the Caputo fractional derivative in time [21], ( ) is the given function and is the linear differential operator. This problem is considered a mathematical model for a wide scope of significant physical phenomena. It has become one of the most important classes of nonlinear equations due to its occurrence in many chemical and biological processes.
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