OPERATIONAL MATRIX METHOD FOR SOLVING NONLINEAR SPACE-TIME FRACTIONAL ORDER REACTION-DIFFUSION EQUATION BASED ON GENOCCHI POLYNOMIAL

An operational matrix method with Genocchi polynomials is derived to solve a space-time fractional order nonlinear reaction-diffusion equation with forced term. Applying a collocation method and using the operational matrix, a fractional order nonlinear partial differential equation is reduced to a system of algebraic equations, which can be solved by using Newton iteration. The salient features of the article are the pictorial presentations of the numerical solution of the concerned equation for different particular cases to show the effect of reaction term on the solution profile and also the change of its behavior when the system goes from standard order to fractional order. The accuracy of our proposed method is validated through the error analysis between the obtained numerical results and the analytical results of two existing standard order models.