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
[PDF]
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.