Fractional Sumudu decomposition method for time-fractional OBBM-Burgers equation with its similarity reduction, conservation laws, and analytical solutions

Abstract The time-fractional Oskolkov-Benjamin-Bona-Mahony-Burgers (TF-OBBMB) equation is investigated in this paper. For this equation, we apply the Lie symmetry analysis to detect the symmetries and the vector fields provided using the definition of Riemann-Liouville (R-L) fractional derivatives. These symmetries allow us to construct the similarity reduction for the considered equation which converts it to a fractional ordinary differential (FOD) equation. Add to that, a set of solutions for the TF-OBBMB equation is obtained by the fractional sub-equation method. Also, we build a numerical solution by using the fractional Sumudu decomposition method in the sense of Caputo fractional derivatives accompanied by the absolute errors and the effect of the fractional-order α. Furthermore, we present a clear explanation for the physical meaning of both analytical and numerical solutions. Finally, we compute the conservation laws in detail in the light of the new conservation theorem.