Abstract
Abstract In this paper, we prove the existence and uniqueness of a mild solution to the system of ψ- Hilfer neutral fractional evolution equations with infinite delay H 𝔻0 αβ;ψ [x(t) − h(t, xt )] = A x(t) + f (t, x(t), xt ), t ∈ [0, b], b > 0 and x(t) = ϕ(t), t ∈ (−∞, 0]. We first obtain the Volterra integral equivalent equation and propose the mild solution of the system. Then, we prove the existence and uniqueness of solution by using the Banach contraction mapping principle and the Leray-Schauder alternative theorem.
Highlights
We prove the existence and uniqueness of solution by using the Banach contraction mapping principle and the Leray-Schauder alternative theorem
In this paper, we consider the following ψ-Hilfer neutral fractional di erential equations with in nite delays: [x(t) h(t, xt )]A x(t) + f (t, x(t), xt), t ∈ [, b], b > (1)x(t) = φ(t), t ∈ (−∞, ] where (.)is the ψ-Hilfer fractional derivative of order< α ≤, with respect to function ψ ∈L([, b], X) and type ≤ β ≤
We prove the existence and uniqueness of the mild solution based on Banach xed point principle and the Leray-Schauder alternative theorem
Summary
We prove the existence and uniqueness of solution by using the Banach contraction mapping principle and the Leray-Schauder alternative theorem. Some of the authors proved the existence and uniqueness of the solution to semilinear neutral type fractional di erential equations with in nite delays by using the Banach Contraction mapping theorem such as [19, 26]. In [18], the authors proved the existence and uniqueness of solution using Banach xed point theorem and the Leray-Schauder Alternative Theorem.
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