Application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity

This work uses the modified Extended Direct Algebraic Method (mEDAM) with conformable derivatives to obtain accurate solutions for the diffusion-reaction equation with cubic nonlinearity and the nonlinear fractional generalised density-independent DR problem. We use fractional derivatives in the conformable sense to achieve precise polynomial-form solutions by converting the equations into autonomous two-dimensional plane systems. The technique solves nonlinear ordinary differential equations (ODEs) produced by a fractional transformation to produce travelling wave solutions. Through the visualisation of various solution profiles, as periodic, shock, kink, anti-kink, and soliton waves, numerical simulations offer important insights into the dynamics of nonlinear fractional partial differential equations. This work builds on earlier research and broadens our understanding of complex events.