Existence results to a <i>ψ</i>- Hilfer neutral fractional evolution equation with infinite delay

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 𝔻 0 αβ;ψ [ x ( t ) − h ( t , x t )] = A x ( t ) + f ( t , x ( t ), x t ), t ∈ [0, b ], b &gt; 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.

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