On the numerical solutions of coupled nonlinear time-fractional reaction-diffusion equations

• Published in: AIMS mathematics Vol. 6; no. 8; pp. 9109 - 9125
• Main Authors: Jannelli, Alessandra, Speciale, Maria Paola
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: caputo derivatives; implicit trapezoidal method; lie symmetries; riemann-liouville fractional derivatives; time-fractional reaction-diffusion equations
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021529

In this paper, we investigate the numerical solutions of coupled nonlinear time-fractional reaction-diffusion equations obtained by applying a procedure that combines the Lie symmetry analysis with the numerical methods. By Lie symmetries, the model, governed by two fractional differential equations defined in terms of the Riemann-Liouville fractional derivatives, is reduced into nonlinear fractional ordinary differential equations that, by introducing the Caputo derivative, are numerically solved by the implicit trapezoidal method. The solutions of the original model are computed by the inverse transformations. Numerical examples are performed in order to show the efficiency and the reliability of the proposed approach applied for solving a wide class of fractional models.