Solution of fractional Sawada–Kotera–Ito equation using Caputo and Atangana–Baleanu derivatives

Abstract

In the present work, the fractional‐order Sawada–Kotera–Ito problem is solved by considering nonlocal Caputo and nonsingular Atangana–Baleanu (ABC) derivatives. The methodology used is an application of the Shehu transform and the Adomian decomposition method. The obtained solution is more accurate when using the ABC type derivative as compared to the Caputo sense, when using the proposed ADShTM method (Adomian decomposition Shehu transform method). The results so obtained by the ADShTM using Caputo and ABC operators are compared, establishing the superiority of the proposed method. The numerical results demonstrate that the application of the ABC derivative is not only relatively more effective and reliable but also straightforward to achieve high precision solution.