In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order [Formula: see text] to higher arbitrary order and we formulate their correspondent integral operators. We prove existence and uniqueness theorems for the Caputo ([Formula: see text]) and Riemann ([Formula: see text]) type initial value problems ...

Abstract In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative non-singular kernel (in the Atangana–Baleanu–Caputo type) is introduced and computational method proposed for its numerical solution. The desired established upon shifted Jacobi polynomials their operational matrix of differentiation (which extracted in present study) together sp...

Abstract In this article, we present a fractional Kersten–Krasil’shchik coupled KdV-mKdV nonlinear model associated with newly introduced Atangana–Baleanu derivative of order which uses Mittag-Leffler function as nonsingular and nonlocal kernel. We investigate the behavior multi-component plasma. For effective approach, named homotopy perturbation, transformation approach is suggested. This sch...

Abstract Our aim in this article is to solve the composite fractional relaxation differential equation by using different definitions of non-integer order derivative operator $D_{t}^{\alpha }$ D t ? , more specifically we employ Caputo, Caputo–Fab...

In this study, we explore a recent biological model created to analyze the behavior of cancer cells by administering dose drug containing anti-PD-L1 and IL-10 with Caputo Atangana–Baleanu derivative in sense (ABC). Using order examine stability non-linear system, are able demonstrate that it is existent unique, introduce several numeric data obtained for fractional values MATLAB using Adams–Bas...

In this paper, we used the natural decomposition approach with non-singular kernel derivatives to find solution nonlinear fractional Gardner and Cahn–Hilliard equations arising in fluid flow. The derivative is considered an Atangana–Baleanu Caputo manner (ABC) Caputo–Fabrizio (CF) throughout paper. We implement transform aid of suggested obtain followed by inverse transform. To show accuracy va...

A mathematical model of the nutrient-phytoplankton-zooplankton associated with viral infection in phytoplankton under Atangana-Baleanu derivative Caputo sense is investigated this study. We prove theoretical results for existence and uniqueness solutions by using Banach’s Sadovskii’s fixed point theorems. The notion various Ulam’s stability used to guarantee context analysis. Furthermore, equil...