Using extended direct algebraic method to investigate families of solitary wave solutions for the space-time fractional modified benjamin bona mahony equation

Abstract This work studies the space-time fractional modified Benjamin-Bona-Mahony equation, a mathematical model of nonlinear wave propagation in various physical systems, for solitary wave solutions. Among the precise solutions we produce with the Extended Direct Algebraic method are solitary waves and periodic wave patterns. These solutions reveal information on soliton interactions and propagation processes, offering insight into the dynamics of the problem. Characterizing the answers is made easier with the use of graphic representations. Our work bridges the gap between chemical reaction-diffusion mechanisms and biological mathematics to improve comprehension of complicated events in interdisciplinary study.