Laplace residual series method for solving fractional Newell–Whitehead–Segel Model

Abstract

In this paper, we present certain Laplace residual power series method as a novel numeric- analytic approach to create approximate and analytic solutions for a fractional Newell-Whitehead-Segel model equipped with appropriate initial space functions. The aforesaid approach depends on coupling the Laplace integral operator together with the generalized Taylor’s formula, where the coefficients of the fractional expansion in the Laplace space is produced by using the limit notion. Numerical experiments are done to guarantee and illustrate the theoretical methodology of the Laplace residual power series LRPS approach. They, also demonstrate its performance, applicability and superiority to solve different kinds of non-linear time and space fractional differential models. The obtained analytical solutions by the present approach agree with other approaches and are compatible with the exact solutions. Numerical simulations of the given results reveal that the LRPS approach is effective, simple and harmonious with the complexity of the non-linear problems.