Korteweg-de Vries-Burgers (KDVB) equation with Atangana-Baleanu derivative with fractional order

Abstract

In this work, we examine the Korteweg–de Vries–Burgers equation with two perturbation’s levels to the concepts of fractional differentiation with no singularity. The Korteweg–de Vries–Burgers equation was constructed using the new fractional differentiation based on the generalized Mittag-Leffler function due to the non-locality. It is presented the existence of a positive set of the solutions for the KDVB equation. The uniqueness of the positive solutions was presented in detail.