An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equation

Abstract

The q-homotopy analysis transform method (q-HATM) is employed to find the solution for the fractional Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology.