Abstract The current paper is about the investigation of a new integral transform introduced recently by Jafari. Specifically, we explore applicability this on Atangana–Baleanu derivative and associated fractional integral. It shown that applying specific conditions transform, other transforms are deduced. We provide examples to reinforce transform.

The aim of this paper is to study a comprehensive dynamics system called fractional fuzzy differential variational inequality, which composed nonlinear equation with Atangana-Baleanu derivative and time-dependent inequality. We explore an existence uniqueness theorem for the under consideration. Our proof based on F-KKM theorem, Banach fixed point principle, theory monotone operators.

The aim of this article is to investigate a coupled hybrid system fractional differential equations with the Atangana–Baleanu–Caputo derivative which contains Mittag–Leffler kernel function in its kernel. We firstly apply Dhage fixed point principle obtain existence mild solutions. Then, we study Ulam–Hyers stability introduced system. Finally, an example presented exhibit validity our results.

This work combines a ZZ transformation with the Adomian decomposition method to solve fractional-order Fokker-Planck equations. The fractional derivative is represented in Atangana-Baleanu derivative. It looked at graphs that show accurate and estimated results are close each other, indicating works. Fractional-order solutions most line dynamics of targeted problems, they provide an endless num...

Abstract We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu senses derivatives. consider existence uniqueness solutions Hyers–Ulam (H-U) stability for class. use Banach Leray–Schauder alternative theorems criteria. With help nonnegative Green’s functions, fractional-order is turned into m -equivalent integral forms. As an app...

This paper presents a new predictor–corrector numerical scheme suitable for fractional differential equations. An improved explicit Atangana–Seda formula is obtained by considering the neglected terms and used as predictor stage of proposed method. Numerical formulas are presented that approximate classical first derivative well Caputo, Caputo–Fabrizio Atangana–Baleanu derivatives. Simulation r...

The functional effects of medications, such as those that slow down and calm the body, have been investigated for polarized diffusion coefficient based on subsequent increase through magnetism. This study examines generalized Mittag–Lefer kernel-based fractional derivatives in MHD Brinkman-type fluids under bioconvection contain hybrid titanium dioxide (TiO 2 ) silver (Ag) nanoparticles with wa...

In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to generalized regularized long wave equations a new fractional operator obtain approximate solutions. We classical differential form by using Atangana-Baleanu derivative which defined Mittag-Leffler function. To show efficiency of proposed method, numerical example given for different v...

Nowadays, fractional derivative is used to model various problems in science and engineering. In this paper, a new numerical method approximate the generalized Hattaf involving nonsingular kernel proposed. This included several forms existing literature such as Caputo–Fabrizio derivative, Atangana–Baleanu weighted derivative. The proposed based on Lagrange polynomial interpolation, it applied s...