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Research Article | Open Access

Existence and controllability of Hilfer fractional neutral differential equations with time delay via sequence method

Krishnan Kavitha1, Velusamy Vijayakumar1, Kottakkaran Sooppy Nisar2( ), Anurag Shukla3, Wedad Albalawi4, Abdel-Haleem Abdel-Aty5,6
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632 014, 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
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia
Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
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Abstract

This paper deals with the existence and approximate controllability outcomes for Hilfer fractional neutral evolution equations. To begin, we explore existence outcomes using fractional computations and Banach contraction fixed point theorem. In addition, we illustrate that a neutral system with a time delay exists. Further, we prove the considered fractional time-delay system is approximately controllable using the sequence approach. Finally, an illustration of our main findings is offered.

Keywords

hilfer fractional derivativeapproximate controllabilityneutral systemtime delaymild solutionssequence approachnonlocal conditions
CLC number: 26A33, 34A08, 47D09, 47H10, 93C43

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 12760-12780
DOI: 10.3934/math.2022706

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Cite this article:
Kavitha K, Vijayakumar V, Nisar KS, et al. Existence and controllability of Hilfer fractional neutral differential equations with time delay via sequence method. AIMS Mathematics, 2022, 7(7): 12760-12780. https://doi.org/10.3934/math.2022706

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Received: 09 March 2022
Revised: 20 April 2022
Accepted: 22 April 2022
Published: 15 July 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)