KORTEWEG-DE VRIES-BURGERS (KDVB) EQUATION WITH ATANGANA-BALEANU DERIVATIVE WITH FRACTIONAL ORDER

KORTEWEG-DE VRIES-BURGERS (KDVB) EQUATION WITH ATANGANA-BALEANU DERIVATIVE WITH FRACTIONAL ORDER

M. A. Dokuyucu

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Abstract

In this work, we examine the Korteweg{de Vries{Burgers equation with two perturbation's levels to the concepts of fractional dierentiation with no singularity. The Korteweg{de Vries{Burgers equation was constructed using the new fractional dieren- tiation based on the generalized Mittag-Leer 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.

Keywords

Korteweg{de Vries{Burgers equation, fractional dierentiation, existence and uniqueness.