A study on controllability of impulsive fractional evolution equations via resolvent operators

In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the ( α , β ) -resolvent operator, we concern with the term u...

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Bibliographic Details
Published in:Boundary value problems 2021-02, Vol.2021 (1), p.1-22, Article 25
Main Authors: Gou, Haide, Li, Yongxiang
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Banach spaces
Controllability
Difference and Functional Equations
Differential equations
Evolutionary computation
Fixed points (mathematics)
Fractional calculus
Mathematics
Mathematics and Statistics
Measure of noncompactness
Mild solution
Mönch fixed point theorem
Ordinary Differential Equations
Partial Differential Equations
Stability
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Summary:In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the ( α , β ) -resolvent operator, we concern with the term u ′ ( ⋅ ) and finding a control v such that the mild solution satisfies u ( b ) = u b and u ′ ( b ) = u b ′ . Finally, we present an application to support the validity study.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-021-01499-5