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.

The development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively recent past. Suitable fixed point theorem to be selected study boundary value due properties exhibited difference operators. This article aims at investigating stability results sense Hyers and Ulam with application Mittag–Leffler function hybrid or...

We will consider the Banach space valued differential equation y′(t) = Ay(t) , where A is an n× n complex matrix. We give a necessary and sufficient condition in order that the equation have the Hyers-Ulam stability. As a Corollary, we prove that the Banach space valued linear differential equation with constant coefficients y(n)(t) + an−1y(n−1)(t) + · · ·+ a1y′(t) + a0y(t) = 0 has the Hyers-Ul...

We solve the inhomogeneous Chebyshev’s differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Chebyshev’s differential equation.

In this paper, we study the existence of solutions for fractional differential equations with Caputo-Hadamard derivative order 2 (1, 2]. The uniqueness result is proved via Banach’s contraction mapping principle and results are established by using Schauder’s fixed point theorem. Furthermore, Ulam-Hyers Ulam-Hyers-Rassias stability proposed equation employed. Some examples given to illustrate r...

The fractional Langevin equation has more advantages than its classical in representing the random motion of Brownian particles complex viscoelastic fluid. Mittag–Leffler (ML) without singularity is accurate and effective Riemann–Caputo (RC) Riemann–Liouville (RL) portraying motion. This paper focuses on a nonlinear ML-fractional system with distributed lag integral control. Employing fixed-poi...

In this paper we present four types of Ulam stability for ordinary differential equations: Ulam-Hyers stability, generalized UlamHyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-HyersRassias stability. Some examples and counterexamples are given.

We argue that Ulam-Hyers stability concept is quite significant in realistic problems in numerical analysis, biology and economics. A generalization to nonlinear systems is proposed and applied to the logistic equation (both differential and difference), SIS epidemic model, Cournot model in economics and a reaction diffusion equation. To the best of our knowledge this is the first time Ulam-Hye...