Existence and stability results for nonlinear fractional delay differential equations

We establish existence and uniqueness results for fractional order delay differential equations. It is proved that successive approximation method can also be successfully applied to study Ulam--Hyers stability, generalized Ulam--Hyers stability, Ulam--Hyers--Rassias stability, generalized Ulam--Hyers--Rassias stability, $\mathbb{E}_{\alpha}$--Ulam--Hyers stability and generalized $\mathbb{E}_{\alpha}$--Ulam--Hyers stability of fractional order delay differential equations

EXISTENCE AND ULAM STABILITY OF SOLUTIONS FOR NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING TWO FRACTIONAL ORDERS

In this paper, we study existence, uniqueness and Ulam-Hyers stability of solutions for integro-differential equations involving two fractional orders. By using Banach's fixed point theorem, we obtain some sufficient conditions for the existence and uniqueness of solution for the mentioned problem. Furthermore, we derive the Ulam-Hyers stability and the generalized Ulam-Hyers stability of solution. At the end, an illustrative example is discussed

On stability for nonlinear implicit fractional differential equations

The purpose of this paper is to establish some  types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of implicit fractional-order differential equation

New sufficient conditions to ulam stabilities for a class of higher order integro-differential equations

In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the sigma-semi-Hyers-Ulam stability, which is in some sense between the Hyers-Ulam and the Hyers-Ulam-Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.publishe

A coupled system of p-Laplacian implicit fractional differential equations depending on boundary conditions of integral type

The objective of this article is to investigate a coupled implicit Caputo fractional $p$-Laplacian system, depending on boundary conditions of integral type, by the substitution method. The Avery-Peterson fixed point theorem is utilized for finding at least three solutions of the proposed coupled system. Furthermore, different types of Ulam stability, i.e., Hyers-Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability, are achieved. Finally, an example is provided to authenticate the theoretical result