ANALYSIS OF TIME-FRACTIONAL BURGERS AND DIFFUSION EQUATIONS BY USING MODIFIED q-HATM

Nehad Ali Shah, Praveen Agarwal (), Jae Dong Chung, Saad Althobaiti (), Samy Sayed, A. F. Aljohani () and Mohamed Alkafafy ()
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Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
Praveen Agarwal: ��Department of Mathematics, Anand International College of Engineering, Jaipur 302003, India
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
Saad Althobaiti: ��Department of Science and Technology, University College — Ranyah, Taif University, Ranyah 21975, Saudi Arabia
Samy Sayed: �Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
A. F. Aljohani: �Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
Mohamed Alkafafy: �Department of Biotechnology, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-12

Abstract: In this paper, the q-homotopy analysis transform technique is implemented to analyze the solution of fractional-order Burgers and diffusion equations with the help of Caputo operator. The results of the proposed method are shown and analyzed with the help of figures. This approach is used to determine the solution in a convergent sequence and illustrate the q-homotopy analysis transform technique solutions convergence to the exact result. Several examples showed the reliability and simplicity of the technique and highlighted the significance of this work. Therefore, the proposed method is successful in investigating other fractional-order linear and nonlinear partial differential equations.

Keywords: q-Homotopy Analysis Transform Method; Elzaki Transform; Caputo Derivatives; Burgers’ and Diffusion Equations (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400126

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