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Research Article | Open Access

A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r ∈ ( 1 , 2 ) with impulses

Marimuthu Mohan Raja1, Velusamy Vijayakumar1, Anurag Shukla2, Kottakkaran Sooppy Nisar3,4( ), Wedad Albalawi5, Abdel-Haleem Abdel-Aty6,7
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India
Department of Applied Science, Rajkiya Engineering College Kannauj, Kannauj-209732, India
Department of Mathematics, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, 16278, Saudi Arabia
School of Technology, Woxsen University- Hyderabad-502345, Telangana State, 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

In this article, we look into the important requirements for exact controllability of fractional impulsive differential systems of order 1 < r < 2. Definitions of mild solutions are given for fractional integrodifferential equations with impulses. In addition, applying fixed point methods, fractional derivatives, essential conditions, mixed Volterra-Fredholm integrodifferential type, for exact controllability of the solutions are produced. Lastly, a case study is supplied to show the illustration of the primary theorems.

Keywords

fractional differential equationscontrollabilityimpulsive systemmeasure of noncompactnessVolterra-Fredholm typesectorial operators
CLC number: 26A33, 34A08, 35R12, 47B12, 47H08, 46E36, 93B05

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 10802-10821
DOI: 10.3934/math.2023548

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Raja MM, Vijayakumar V, Shukla A, et al. A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r ∈ ( 1 , 2 ) with impulses. AIMS Mathematics, 2023, 8(5): 10802-10821. https://doi.org/10.3934/math.2023548

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Received: 07 January 2023
Revised: 21 February 2023
Accepted: 22 February 2023
Published: 15 May 2023
©2023 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)