Analytical Solutions of the Nonlinear Time-Fractional Coupled Boussinesq-Burger Equations Using Laplace Residual Power Series Technique

In this paper, we present the series solutions of the nonlinear time-fractional coupled Boussinesq-Burger equations (T-FCB-BEs) using Laplace-residual power series (L-RPS) technique in the sense of Caputo fractional derivative (C-FD). To assert the efficiency, simplicity, performance, and reliability of our proposed method, an attractive and interesting numerical example is tested analytically and graphically. In addition, our obtained results show that this algorithm is compatible and accurate for investigating the fractional-order solutions of engineering and physical applications. Finally, Mathematica software 14 is applied to compute the numerical and graphical results.

Automated summary

This paper presents the series solutions of the nonlinear time-fractional coupled Boussinesq-Burger equations using the Laplace-residual power series technique. An attractive numerical example is used to verify the efficiency and reliability of the proposed method. The obtained results demonstrate the compatibility and accuracy of this algorithm for fractional-order solutions in engineering and physical applications.