A new approach on approximate controllability of fractional evolution inclusions of order 1 < r < 2 with infinite delay

M. Mohan Raja, V. Vijayakumar and R. Udhayakumar

Chaos, Solitons & Fractals, 2020, vol. 141, issue C

Abstract: This manuscript is mainly focusing on the approximate controllability of fractional differential evolution inclusions of order 1 < r < 2 with infinite delay. We study our primary outcomes by using the theoretical concepts about fractional calculus, cosine, and sine function of operators and Dhage’s fixed point theorem. Initially, we prove the approximate controllability for the fractional evolution system. The results are established under the assumption that the associated linear system is approximately controllable. Then, we develop our conclusions to the ideas of nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study.

Keywords: Approximate controllability; Fractional derivative; Infinite delay; Mild solutions; Mainardi’s Wright-type function (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307384

DOI: 10.1016/j.chaos.2020.110343

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