Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay

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 H𝔻0αβ;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.

Keywords

• ψ-hilfer fractional derivative
• infinite delays
• mild solution
• banach contraction principle
• leray-schauder alternative
• 34a08
• 34a12
• 34g99
• 34k99