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Research Article | Open Access

Results on controllability for Sobolev type fractional differential equations of order 1 < r < 2 with finite delay

Yong-Ki Ma1, Marimuthu Mohan Raja2, Kottakkaran Sooppy Nisar3, Anurag Shukla4, Velusamy Vijayakumar2( )
Department of Applied Mathematics, Kongju National University, Chungcheongnam-do 32588, Republic of Korea
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
Department of Applied Science, Rajkiya Engineering College Kannauj, Kannauj 209732, India
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Abstract

In this article, exact controllability results for Sobolev fractional delay differential system of 1 < r < 2 are investigated. Fractional analysis, cosine and sine function operators, and Schauder's fixed point theorem are applied to verify the main results of this study. To begin, we use sufficient conditions to explore the controllability for fractional evolution differential system with finite delay. Lastly, an example is provided to illustrate the obtained theoretical results.

Keywords

fractional differential systemscontrollabilityMainardi's Wright-type functionSobolev typemild solutions
CLC number: 34A08, 26A33, 93B05, 46E36, 47D09

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10215-10233
DOI: 10.3934/math.2022568

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Ma Y-K, Raja MM, Nisar KS, et al. Results on controllability for Sobolev type fractional differential equations of order 1 < r < 2 with finite delay. AIMS Mathematics, 2022, 7(6): 10215-10233. https://doi.org/10.3934/math.2022568

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Received: 13 November 2021
Revised: 13 March 2022
Accepted: 15 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)