Construction of fractional series solutions to nonlinear fractional reaction–diffusion for bacteria growth model via Laplace residual power series method

• Published in: International journal of dynamics and control Vol. 11; no. 2; pp. 520 - 527
• Main Authors: Oqielat, Moa’ath N., Eriqat, Tareq, Al-Zhour, Zeyad, Ogilat, Osama, El-Ajou, Ahmad, Hashim, Ishak
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023; Springer Nature B.V
• Subjects: Algorithms; Bacteria; Complexity; Control; Control and Systems Theory; Diffusion; Dynamical Systems; Engineering; Power series; Vibration; Laplace residual power series method; Approximate series solutions; Reaction–diffusion for bacteria growth model; Caputo fractional derivative
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-022-01001-8

In this paper, a new Laplace residual power series (LRPS) algorithm has been constructed to yield approximate series solutions (ASSs) of the nonlinear fractional differential system (NFDS) in the sense of Caputo derivative (CD). To show the effectiveness of our technique, we present the ASSs of an attractive biological and physical problem which is related to the nonlinear fractional reaction–diffusion for bacteria growth system (NFR-DBGS). To validate the accuracy of our proposed algorithm, we make a comparison between the numerical results of the LRPS method and Adomian decomposition method (ADM) at different values of α . Finally, the classical behavior of this problem has been also recovered when α = 1 .