OPTIMAL EXISTENCE AND SOLITARY WAVE STRUCTURE OF GIERER–MEINHARDT ACTIVATOR–SUBSTRATE MODEL

In this research, we investigate the pattern formation generated by the fractional order reaction and diffusion systems of nonlinear partial differential equations. We analyze the existence of the solutions in closed and convex subsets of function spaces for the fractional Gierer–Meinhardt system using different optimal approaches. We apply an analytical technique to extract the exact solitary wave solutions. We use traveling wave transformation to reduce the system. These solutions are in terms of hyperbolic, parabolic, trigonometric, and some mixed functions. The proposed strategy to obtain the soliton results is a generalized exponential rational function method (GERFM). We comparatively discuss the behavior of the achieved solitons. To show the nature of the waves, 2-D and 3-D plots with their contours are drawn.