Stability of Ulam–Hyers and Ulam–Hyers–Rassias for a class of fractional differential equations

Abstract

In this paper, we investigate a class of nonlinear fractional differential equations with integral boundary condition. By means of Krasnosel'skiȋ fixed point theorem and contraction mapping principle we prove the existence and uniqueness of solutions for a nonlinear system. By means of Bielecki-type metric and the Banach fixed point theorem we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stability of nonlinear fractional differential equations. Besides, we discuss an example for illustration of the main work.

A fractional differential equation with multi-point strip boundary condition involving the Caputo fractional derivative and its Hyers–Ulam stability

“…Dai et al [37] studied the Caputo fractional derivative along with HUS and HURS for a class of FDEs of the following integral boundary condition:…”

“…Motivated by the work introduced in [34][35][36][37], in this paper, we study the existence and uniqueness, HUS and HURS of the accompanying nonlinear FDE including Caputo fractional derivative. The proposed framework is as follows:…”

Fractional Fourier transform and stability of fractional differential equation on Lizorkin space

“…In [25], a study on the H-U stability condition was conducted, focusing on an impulsive R-L fractional neutral functional stochastic differential equation with time delays. In [26], the stability criteria pertaining to a class of fractional differential equations was investigated, in which the Krasnoselskii fixed point method was employed. Recently, Opadhyay et al [27] discussed the R-L fractional differential equations using the Hankel transform method.…”

On multidimensional fractional Langevin equations in terms of Caputo derivatives

“…Furthermore, Ulam-Hyers stability is one of the important issues in the theory of differential equations and their applications. Considerable work have been done in this field of research, see, e.g., Abbas et al [1], Chalishajar [4], Dai et al [6], Harikrishnan et al [10], Ibrahim et al [11], Taïeb [24][25][26][27][28], Taïeb et al [29][30][31] and Wang [33].…”