Existence results and Ulam–Hyers stability to impulsive coupled system fractional differential equations

Abstract

In this paper, the existence and uniqueness of the solutions to impulsive coupled system of fractional differential equations with Caputo-Hadamard are investigated. Furthermore, Ulam's type stability of the proposed coupled system is studied. The approach is based on a Perov type fixed point theorem for contractions.

Existence and Ulam‐type stability for impulsive oscillating systems with pure delay

“…In [29], the authors obtained the existence and UHs of the solution to a class of implicit fractional differential equations with impulsive conditions. In [30], the authors studied the existence, uniqueness, and Ulam's type stability of the solution for fractional impulsive coupled system. In [31], the authors studied the existence and uniqueness of the solution for fractional differential equation involving Caputo Hadamard fractional operator of order $$$ 1<\vartheta \le 2 $$$ with impulsive boundary conditions.…”

Hyers–Ulam Stability of a System of Hyperbolic Partial Differential Equations

“…We specify that Hyers-Ulam stability for coupled fixed points of contractive-type operators have been studied, for example, in [25,26] and Hyers-Ulam stability for coupled systems of fractional differential equations in [27][28][29].…”

Existence and Uniqueness Results of Coupled Fractional-Order Differential Systems Involving Riemann–Liouville Derivative in the Space Wa+γ1,1(a,b)×Wa+γ2,1(a,b) with Perov’s Fixed Point Theorem

“…Perov, in 1965, extended the Banach contraction principle to the vector-valued metric spaces by replacing the contraction factor with a matrix that converges to zero [6]. Perov's fixed point theorem is one of the crucial methods to prove an existence solution of systems of differential equations, fractional differential equations, and integral equations in N variables; see [7][8][9][10], and the references cited therein.…”