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Afshin Babaei

Afshin Babaei

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-6980-9786
Education: PhD.
ScopusId: https://www.scopus.com/authid/detail.uri?authorId=57188696707
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran
Phone: 011-35302418

Research

Title
Solving fractional Allen-Cahn equation and the fractional Burger-Fisher equation by using fractional reduced differential transform method
Type
Thesis
Keywords
Non-linear partial differential equation, Allen-Cahn equation, Burger-Fisher equation, Caputo fractional derivative
Year
2023
Researchers Azhar Hamzah Abdullah(Student)، ُSeddighe Banihashemi(Advisor)، Afshin Babaei(PrimaryAdvisor)

Abstract

The main purpose of this thesis is to solve two special classes of nonlinear partial differential equations, the Allen-Cahn equation and the Burger-Fisher equation, using the fractional reduced differential transform method (FRDTM). We implement the proposed computational approach in some test problems. Also, we investigate the applicability and effectiveness of the presented method. At the first stage, the FRDTM is used to acquire approximate solutions of the time fractional-order diffusion equation and two special cases of Allen-Cahn equations. At the second stage, the FRDTM is used to evaluate the time-fractional generalized Burger-Fisher equation (TF-GBFE). To determine the validity of the method, when the solutions are obtained, they are compared to exact solutions of order α=1 , and even for various values of α. Three-dimensional graphs are used to depict the solutions. The analysis of exact and FRDTM solutions indicates that the proposed approach is very accurate.