A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

This work aims to propose a new analyzing tool, called the fractional iteration algorithm I for finding numerical solutions of nonlinear time fractional-order Cauchy reaction-diffusion model equations. The key property of the suggested technique is its ability and flexibility to investigate linear a...

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Bibliographic Details
Published in:	Results in physics Vol. 19; p. 103462
Main Authors:	Ahmad, Hijaz, Khan, Tufail A., Ahmad, Imtiaz, Stanimirović, Predrag S., Chu, Yu-Ming
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.12.2020 Elsevier
Subjects:	Caputo derivative Cauchy reaction-diffusion equation Fractional iteration algorithm-I Nonlinear fractional PDE Nonlinear fractional PDE Caputo derivative Cauchy reaction-diffusion equation Fractional iteration algorithm-I
ISSN:	2211-3797, 2211-3797
Online Access:	Get full text
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Summary:	This work aims to propose a new analyzing tool, called the fractional iteration algorithm I for finding numerical solutions of nonlinear time fractional-order Cauchy reaction-diffusion model equations. The key property of the suggested technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The proposed approach can be utilized without the use of any transformation, Adomian polynomials, small perturbation, discretization or linearization. The main feature of the fractional iteration algorithm-I is the improvement of an auxiliary parameter that can ensure a rapid convergence. To check the stability, accuracy and speed of the method, obtained results are compared numerically and graphically with the exact solutions and results available in the latest literature. In addition, numerical results are displayed graphically for various cases of the fractional-order α. These results demonstrate the viability of the proposed technique and show that this technique is exceptionally powerful and suitable for solving fractional PDEs.
ISSN:	2211-3797 2211-3797
DOI:	10.1016/j.rinp.2020.103462