Adaptation on power series method with conformable operator for solving fractional order systems of nonlinear partial differential equations.

The aim of this research work is to modify the power series solution method to fractional order in the sense of conformable derivative to solve a coupled system of nonlinear fractional partial differential equations. We called it the conformable fractional power series method. To evaluate its efficiency and consistency, absolute errors of three problems are considered numerically. Consequences established that our recommended method is unpretentious, accurate, valid, and capable. When solving the nonlinear complications, it has a powerful superiority over the homotopy analysis and Adomian decomposition methods. Additional as in the residual power series method through generating the coefficients for a series, it is compulsory to calculate the fractional derivatives on every occasion, whereas this method only needs the idea of equating coefficients. The convergence and error analyses of the series solutions are also presented. • We construct the power series solution method to investigate the integer and fractional order linear differential equations. • We obtain the approximate and exact solutions of the equations. • We demonstrate the simulations. [ABSTRACT FROM AUTHOR]