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Keywords = non-autonomous fractional evolution equations

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18 pages, 293 KB  
Article
Existence and Controls for Fractional Evolution Equations
by Ying Chen and Yong Zhou
Axioms 2025, 14(5), 329; https://doi.org/10.3390/axioms14050329 - 24 Apr 2025
Viewed by 429
Abstract
In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermore, the optimal control of nonlinear NFEEs with integral index functionals [...] Read more.
In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermore, the optimal control of nonlinear NFEEs with integral index functionals is studied, and the existence of optimal control pairs is proven. Finally, by constructing a corresponding Gramian controllability operator using the solution operator, a sufficient condition is provided for the existence of approximate controllability of the corresponding problem. Full article
(This article belongs to the Special Issue Nonlinear Fractional Differential Equations: Theory and Applications)
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