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

• Main Authors: Hijaz Ahmad, Tufail A. Khan, Imtiaz Ahmad, Predrag S. Stanimirović, Yu-Ming Chu
• Format: Article
• Language: English
• Published: Elsevier 2020-12-01
• Series: Results in Physics
• Subjects: Fractional iteration algorithm-I; Caputo derivative; Cauchy reaction-diffusion equation; Nonlinear fractional PDE
• Online Access: http://www.sciencedirect.com/science/article/pii/S2211379720319215

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.