Theory and application for the time fractional Gardner equation with Mittag-Leffler kernel

Abstract

In this work, the time fractional Gardner equation is presented as a new fractional model for Atangana–Baleanu fractional derivative with Mittag-Leffler kernel. The approximate consequences are analysed by applying a recurrent process. The existence and uniqueness of solution for this system is discussed. To explain the effects of several parameters and variables on the movement, the approximate results are shown in graphics and tables.

Keywords

• the time fractional gardner equation
• atangana–baleanu derivative
• mittag-leffler kernel
• existence and uniqueness
• series solution