Stability analysis of semi-analytical technique for time-fractional Cauchy reaction-diffusion equations

Abstract In this article, classical Cauchy reaction-diffusion equations are converted into the corresponding time-fractional Cauchy reaction-diffusion equations using Caputo–Fabrizio fractional order derivative. The obtained equations are then solved using a semi-analytical method, which is the combination of Laplace transform and Picard’s iterative scheme. The derived solutions are innovative, and such derivations are not found in the previous literature. In addition, the Banach fixed-point principle and G -stable mapping are used to analyze stability of the implemented semi-analytical method. Error estimation and comparison of derived results with exact solutions already available in the literature through graphical illustrations and tables reveal that the implemented semi-analytical method is more efficient and fruitful for solution of time-fractional Cauchy reaction-diffusion equations.