An innovative method for solving the nonlinear fractional diffusion reaction equation with quadratic nonlinearity analysis

Abstract This study generates and investigates spreading solitons in the fractional DR quadratic equation (FDE) with fractional derivatives using the Extended Direct Algebraic Method (EDAM). In population growth, mathematical biology, and reaction-diffusion mechanisms, the FDE is crucial. Applying the series form solution to the NODE from the FDE conversion into a recommended EDAM yields many traveling soliton solutions. To characterize and explore soliton structure propagation, we draw shock and kink soliton solutions. Through reaction-diffusion mechanics and mathematical biology, we may explain complex processes in many academic subjects.