Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator

Abstract

In this paper, the dynamic process of pulse-splitting patterns is reported in fractional medium. In the classical Gray-Scott system, the integer-order derivative is replaced with the known Atangana-Baleanu fractional order derivative in the sense of Caputo. mathematical analysis such as the existence of stationary solutions for pulse-splitting process, existence and uniqueness of solutions for the fractional system are presented. The beauty of the work is further demonstrated by presenting numerical results for different values of γ in one dimensional space. We deduced from the numerical experiments that pulse-splitting patterns in both integer and noninteger order scenarios are almost the same.