Solution for fractional potential KdV and Benjamin equations using the novel technique

Abstract In this paper, we find the solutions for fractional potential Korteweg–de Vries (p-KdV) and Benjamin equations using q -homotopy analysis transform method ( q -HATM ) . The considered method is the mixture of q -homotopy analysis method and Laplace transform, and the Caputo fractional operator is considered in the present investigation. The projected solution procedure manipulates and controls the obtained results in a large admissible domain. Further, it offers a simple algorithm to adjust the convergence province of the obtained solution. To validate the q -HATM is accurate and reliable, the numerical simulations have been conducted for both equations and the outcomes are revealed through the plots and tables. Comparison between the obtained solutions with the exact solutions exhibits that, the considered method is efficient and effective in solving nonlinear problems associated with science and technology.