Numerical Solution of Time-fractional BBMB Equation via LRPSM

Abstract

The time-fractional Benjamin-Bona-Mahony-Burger (BBMB) differential equation plays an important role in explaining the unidirectional propagation of long waves in definite nonlinear differential systems. This work presents an analytical numerical solution of considered equation by Laplace transform with residual power series method (LRPSM) which is a generalized Taylor series together with Laplace transform and the residual error function. Using the proposed approach, the series solution of this equation is obtained. The analytical numerical solution shows that the LRPSM is a reliable and powerful method for solving the time fractional differential equations (FDEs) with less number of terms. The obtained results of numerical solutions are also compared with the exact solution and presented as absolute errors at different time levels.