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Controllability of Impulsive Fractional Integro-Differential Evolution Equations

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Abstract

In this paper, we are concerned with the controllability for a class of impulsive fractional integro-differential evolution equation in a Banach space. Sufficient conditions of the existence of mild solutions and approximate controllability for the concern problem are presented by considering the term \(u'(\cdot )\) and finding a control \(v\) such that the mild solution satisfies \(u(b)=u_{b}\) and \(u'(b)=u'_{b}\). The discussions are based on Mönch fixed point theorem as well as the theory of fractional calculus and \((\alpha ,\beta )\)-resolvent operator. Finally, an example is given to illustrate the feasibility of our results.

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Acknowledgements

The authors would like to thank the referees for their useful suggestions which have significantly improved the paper.

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  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Haide Gou & Yongxiang Li

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  1. Haide Gou
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  2. Yongxiang Li
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Correspondence to Haide Gou.

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Supported by the National Natural Science Foundation of China (Grant No. 12061062, 11661071).

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Gou, H., Li, Y. Controllability of Impulsive Fractional Integro-Differential Evolution Equations. Acta Appl Math 175, 5 (2021). https://doi.org/10.1007/s10440-021-00433-2

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