Abstract
In this paper, we study the sufficient conditions for the approximate controllability of finite delay fractional functional integro-differential equations with nonlocal condition in a Hilbert space. We use the theory of fractional calculus, semigroup theory, \(\alpha \)-norm, fractional power theory and Krasnoselskii’s fixed point theorem to obtain the results under the assumption that the corresponding linear system is approximate controllable. An example is presented to illustrate the main result.
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Acknowledgments
We are grateful to the referees for their valuable comments and suggestions to this paper. The first author would like to acknowledge the financial assistance provided by University Grant Commission (UGC) of India for carrying out this work. The second author would like to acknowledge that this work has been carried under the Research Project SR/S4/MS:796/12 of DST, New Delhi.
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Jeet, K., Bahuguna, D. & Shukla, R.K. Approximate Controllability of Finite Delay Fractional Functional Integro-Differential Equations with Nonlocal Condition. Differ Equ Dyn Syst 27, 423–437 (2019). https://doi.org/10.1007/s12591-016-0284-z
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DOI: https://doi.org/10.1007/s12591-016-0284-z