Numerical and Analytical Investigation for Solutions of Fractional Oskolkov-Benjamin-Bona-Mahony-Burgers Equation Describing Propagation of Long Surface Waves

Abstract

In this article, a novel meshless numerical scheme to solve the time-fractional OskolkovBenjamin-Bona-Mahony-Burgers equation has been proposed. This equation able to describe many nonlinear phenomena such as analysis of the long-wavelength surface waves in liquids, acoustic-gravity waves in compressible fluids and hydromagnetic waves in cold plasma. The proposed numerical scheme is based on finite difference and Kansa-radial basis function collocation approach. Firstly, the finite difference scheme has been employed to discretize the timefractional derivative and subsequently, the Kansa method is utilized to discretize the spatial derivatives. The stability and convergence of the proposed numerical scheme are also elucidated in this article. Also, the Kudryashov technique has been used to obtain the soliton solutions for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme.