Existence and stability results for nonlinear fractional integrodifferential coupled systems

Abstract

In this paper, a class of nonlinear ψ-Hilfer fractional integrodifferential coupled systems on a bounded domain is investigated. The existence and uniqueness results for the coupled systems are proved based on the contraction mapping principle. Moreover, the Ulam–Hyers–Rassias, Ulam–Hyers, and semi-Ulam–Hyers–Rassias stabilities to the initial value problem are obtained.

Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam–Hyers stability and travelling waves

“…For more details on the FC, one can see [17,23,24]. In fact, many researchers have devoted themselves to investigate fractional order differential equations and systems with different boundary conditions, for more details, the reader can see the works [1,3,4,6,9,10,14,20,22,29,[37][38][39]41].…”

Study of Nonlocal Multiorder Implicit Differential Equation Involving Hilfer Fractional Derivative on Unbounded Domains

“…Ali et al [27] discussed the stability of pantograph-type implicit fractional diferential equations with impulsive conditions. Also, the existence, uniqueness, and UH stabilities result for a coupled ψ− Hilfer fractional integrodiferential equation on bounded domains investigated by [28]. Almalahi et al [29,30] established qualitative theories for fractional functional diferential equation with boundary condition and fnite delay as well as a coupled system of hybrid fractional diferential equations via ϕ− Hilfer fractional derivatives.…”