Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations

Abstract

We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM) partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved $\left({\mathrm{G}}^{\mathrm{\text{'}}}/\mathrm{G}\right)$-expansion function method to find exact solutions of nonlinear fractional BBM equation.