Evaluation of time-fractional Fisher's equations with the help of analytical methods

• DOI: 10.3934/math.20221031
• Publication Date: 2022-08-23T11:06:56Z
• Authors: Ahmed M. Zidan; Adnan Khan; Rasool Shah; Mohammed Kbiri Al...; Wajaree Weera
• Keywords: Decomposition method (queueing theory); Economics; yang transform decomposition method; 01 natural sciences; Convergence Analysis of Iterative Methods for Nonlinear Equations; Differential equation; Computer security; Numerical Analysis; Physics; Mathematical optimization; Statistics; Rate of convergence; Power (physics); Algorithm; Fractional Derivatives; Reliability (semiconductor); homotopy perturbation yang transform method; caputo operator; Modeling and Simulation; Physical Sciences; Convergence (economics); Medicine; Calculus (dental); Iterative Methods; Mathematical analysis; Quantum mechanics; QA1-939; FOS: Mathematics; 0101 mathematics; Homotopy perturbation method; Key (lock); time-fractional fisher's equation; Anomalous Diffusion Modeling and Analysis; Economic growth; Time-Fractional Diffusion Equation; FOS: Clinical medicine; Fractional calculus; Pure mathematics; Statistical and Nonlinear Physics; Applied mathematics; Computer science; Homotopy analysis method; Physics and Astronomy; Dentistry; Fractional Calculus; Adomian decomposition method; Homotopy Analysis Method; Homotopy; Mathematics; Rogue Waves in Nonlinear Systems

<abstract><p>This article shows how to solve the time-fractional Fisher's equation through the use of two well-known analytical methods. The techniques we propose are a modified form of the Adomian decomposition method and homotopy perturbation method with a Yang transform. To show the accuracy of the suggested techniques, illustrative examples are considered. It is confirmed that the solution we get by implementing the suggested techniques has the desired rate of convergence towards the accurate solution. The main benefit of the proposed techniques is the small number of calculations. To show the reliability of the suggested techniques, we present some graphical behaviors of the accurate and analytical results, absolute error graphs and tables that strongly agree with each other. Furthermore, it can be used for solving fractional-order physical problems in various fields of applied sciences.</p></abstract>