Computation of solution to fractional order partial reaction diffusion equations

Haji Gul; Hussam Alrabaiah; Sajjad Ali; Kamal Shah; Shakoor Muhammad

doi:10.1016/j.jare.2020.04.021

Computation of solution to fractional order partial reaction diffusion equations

J Adv Res. 2020 May 15:25:31-38. doi: 10.1016/j.jare.2020.04.021. eCollection 2020 Sep.

Authors

Haji Gul¹, Hussam Alrabaiah^{2

3}, Sajjad Ali⁴, Kamal Shah⁵, Shakoor Muhammad¹

Affiliations

¹ Department of Mathematics, Abdul Wali Khan Univeristy, Mardan, Pakistan.
² College of Engineering, Al Ain University, Al Ain, United Arab Emirates.
³ Department of Mathematics, Tafila Technical University, Tafila, Jordan.
⁴ Department of Mathematics, Shaheed Benazir Bhutto University Sheringal, Dir(U), Pakistan.
⁵ Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan.

Abstract

In this article, the considered problem of Cauchy reaction diffusion equation of fractional order is solved by using integral transform of Laplace coupled with decomposition technique due to Adomian scheme. This combination led us to a hybrid method which has been properly used to handle nonlinear and linear problems. The considered problem is used in modeling spatial effects in engineering, biology and ecology. The fractional derivative is considered in Caputo sense. The results are obtained in series form corresponding to the proposed problem of fractional order. To present the analytical procedure of the proposed method, some test examples are provided. An approximate solution of a fractional order diffusion equation were obtained. This solution was rapidly convergent to the exact solution with less computational cost. For the computation purposes, we used MATLAB.

Keywords: 35A22; 35A25; 35K57; Caputo operator; Decomposition technique; Fractional order CRDE; LADM.

Publication types

Review