A robust analytical approach to the generalized Burgers–Fisher equation with fractional derivatives including singular and non-singular kernels

Abstract

This paper presents a new heuristic approach for the approximate solution of the generalised Burgers–Fisher problem with two distinct derivative senses: Caputo fractional derivative (C) with a singular kernel and Atangana–Baleanu fractional derivative in Caputo sense (ABC) with a non-singular (Mittag–Leffler kernel) kernel. The proposed method is based on the η-homotopy analysis method with a new integral transform, and a well-proven algorithm that quickly provides the approximate solutions and maintains excellent accuracy. Comparative studies have been carried out to check the consistency of the proposed technique with previous methodologies in the literature. Finally, the convergence analysis of the study has been derived and studied the solutions’ behaviour in two different derivative senses having fractional-order μ→1.