Title: Approximate Controllability of Fractional Evolution Equations with Nonlocal Conditions via Operator Theory Show Chinese title

Title: 分数演化方程在非局部条件下的近似能控性通过算子理论

Abstract: This paper investigates the existence and uniqueness of mild solutions, as well as the approximate controllability, of a class of fractional evolution equations with nonlocal conditions in Hilbert spaces. Sufficient conditions for approximate controllability are established through a novel approach to the approximate solvability of semilinear operator equations. The methodology utilizes Green's function and constructs a control function based on the Gramian controllability operator. The analysis is based on Schauder's fixed point theorem and the theory of fractional order solution operators and resolvent operators. To demonstrate the feasibility of the proposed theoretical results, an illustrative example is provided. Show Chinese abstract

Abstract: 本文研究了希尔伯特空间中一类具有非局部条件的分数阶演化方程的温和解的存在性与唯一性，以及近似能控性。 通过一种新的方法建立了近似能控性的充分条件，该方法针对半线性算子方程的近似可解性。 该方法利用格林函数，并基于格拉姆能控性算子构造一个控制函数。 分析基于沙德纳不动点定理以及分数阶解算子和预解算子理论。 为了展示所提出的理论结果的可行性，提供了一个示例。