Analytical approach for fractional extended Fisher–Kolmogorov equation with Mittag-Leffler kernel

Abstract

Abstract A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed with Atangana–Baleanu (AB) operator, and the technique we consider is a mixture of the q-homotopy analysis scheme and the Laplace transform. The fixed point hypothesis is considered for the existence and uniqueness of the obtained solution of this model. For the validation and effectiveness of the projected scheme, we analyse the FEFK equation in terms of arbitrary order for the two distinct cases. Moreover, numerical simulation is demonstrated, and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.

Keywords

• Extended Fisher–Kolmogorov equation
• Atangana–Baleanu derivative
• Fixed point theorem
• Laplace transform
• q-Homotopy analysis method