On the qualitative study of an abstract fractional functional differential equation via the Ψ-Hilfer derivative
Abstract
In this article, we investigate the existence, uniqueness, and Ulam-Hyers stability of the equation:
HD0α,β;Ψ(u(t)+g(t,u(t)))=Au(t) +f(t,u(t)), t ∈ [0,T], with initial condition I1−γ;Ψ0+ u(0)=u0,where HD0α,β;Ψ is the Ψ-Hilfer operator. We use the Banach fixed point principle and the Krasnoselskii's fixed point theorem to achieve our results. We also investigate the stability of this equation. Our results generalize some recent ones on the subject.
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Copyright (c) 2024 L. Kadhim, M.M. Etefa, G.M. N'Guerekata
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