Abstract
In this paper, by using the fractional power of an operator and some fixed point theorems, we study the existence of mild solutions for the nonlocal problem of Caputo fractional impulsive neutral evolution equations in Banach spaces. In the end, an example is given to illustrate the applications of the abstract results. MSC:34K45, 35F25.
Highlights
During the past two decades, fractional differential equations have been proved to be valuable tools in the modeling of many phenomena in various fields of engineering, physics, and economics, and they have gained considerable attention
By using some fixed point theorems of compact operator, they derive many existence and uniqueness results concerning the mild solutions for problem ( ) under the different assumptions on the nonlinear term f
In Section, we study the existence of mild solutions of the problem ( )
Summary
During the past two decades, fractional differential equations have been proved to be valuable tools in the modeling of many phenomena in various fields of engineering, physics, and economics, and they have gained considerable attention. In a Banach space X, where a > is a constant, Dq denotes the Caputo fractional derivative of order q ∈ ( , ), A : D(A) ⊂ X → X is a closed linear operator and –A generates a C -semigroup T(t) (t ≥ ) in X, f : J × X → X is continuous, yk, u are the elements of X, = t < t < t < · · · < tm < tm+ = a, u(tk+) and u(tk–) represent the right and left limits of u(t) at t = tk, respectively. (H ) T(t) (t ≥ ) is a compact analytic semigroup; (H ) The function h : J × Xα → X is continuous and there exists a constant L > such that.
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