TRAVELING WAVE SOLUTIONS TO THE NONLINEAR SPACE-TIME FRACTIONAL KOLMOGOROV PETROVSKII–PISKUNOV EQUATION VIA EFFICIENT ANALYTICAL APPROACHES

Large-scale simulation of nonlinear phenomena in science, engineering, and technology requires the use of nonlinear fractional-order evolution equations. The nonlinear space-time fractional Kolmogorov Petrovskii–Piskunov equation defined in the sense of Jumarie’s modified Riemann–Liouville is discussed in this paper. Kolmogorov–Petrovskii–Piskunov equation can be regarded as a generalized form of the Fitzhugh–Nagumo, Fisher and Huxley equations which have many applications in mathematical biology, reaction–diffusion systems, and population dynamics. By using fractional wave transformation, the model is transformed into a nonlinear equation. This paper uses the Khater and Bernoulli Sub-ODE method to solve the fractional Kolmogorov Petrovskii–Piskunov equation analytically. By using BS-ODE and Khater method, a number of creative solutions have been developed such as the cuspon, V-shaped, kink wave, smooth kink, periodic wave, bright, anti-peakon, and singular soliton solutions. Using constant parameter values, 3D, 2D and contour plots of the solutions are created in order to verify the physical properties of the established solitons. For physical significance, applications of proposed analysis are given in this paper. Properties of proposed methods are also discussed in this work. With the systematic use of these methods, different explicit solutions are developed, which exhibit the underlying wave structures of the fractional Kolmogorov Petrovskii–Piskunov equation. The solutions obtained are also examined for stability and physical significance. A comparative study of the efficiency, applicability, and limitation of both methods is also presented, noting their strengths and possible weaknesses in solving nonlinear fractional partial differential equations.