Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative

Abstract

This work presents analysis of the logarithmic-KdV equation involving new fractional operator called Atangana–Baleanu (AB) fractional derivative with Mittag-Leffler (ML) type kernel. The existence and uniqueness of the governing equation having AB fractional derivative with ML type kernel is proved with the aid of a fixed-point theorem. We present numerical simulations by using iterative algorithm. The effectiveness of various parameters and variables on the displacement are presented in Figures 1 and 2.