Invariant and simulation analysis to the time fractional Abrahams - Tsuneto reaction diffusion system

Abstract

In this work, symmetry analysis and numerical approximations to the time fractional Abrahams–Tsuneto reaction diffusion system (ATRDS) are discussed. We obtain point symmetries, similarity variables, similarity transformation and reduce the time-fractional ATRDS to time-fractional systems of ordinary differential equations. In the reduced equation, the derivative is in Erdelyi–Kober sense. The numerical analysis and simulations are performed using a powerful iterative method called residual power series (RPS) method. The validity and correctness of the RPS method is illustrated by analyzing the approximate solutions graphically and comparing the approximates solutions with exact solutions in tables 1 and 2. The given examples in this paper confirm that the RPS can be used as an alternative for finding approximate solutions for fractional equations. The generalization of ATRDS to time fractional derivative was not reported previously, to the best of our knowledge it is reported for the first time in this research.

In this work, symmetry analysis and numerical approximations to the time fractional Abrahams–Tsuneto reaction diffusion system (ATRDS) are discussed. We obtain point symmetries, similarity variables, similarity transformation and reduce the time-fractional ATRDS to time-fractional systems of ordinary differential equations. In the reduced equation, the derivative is in Erdelyi–Kober sense. The numerical analysis and simulations are performed using a powerful iterative method called residual power series (RPS) method. The validity and correctness of the RPS method is illustrated by analyzing the approximate solutions graphically and comparing the approximates solutions with exact solutions in tables 1 and 2. The given examples in this paper confirm that the RPS can be used as an alternative for finding approximate solutions for fractional equations. The generalization of ATRDS to time fractional derivative was not reported previously, to the best of our knowledge it is reported for the first time in this research.