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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Veröffentlicht in:Results in physics Jg. 19; S. 103462
Hauptverfasser: Ahmad, Hijaz, Khan, Tufail A., Ahmad, Imtiaz, Stanimirović, Predrag S., Chu, Yu-Ming
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.12.2020
Elsevier
Schlagworte:
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
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Zusammenfassung: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