Discussion on iterative process of nonlocal controllability exploration for Hilfer neutral impulsive fractional integro-differential equation

Kanagaraj Muthuselvan; Baskar Sundaravadivoo; Kottakkaran Sooppy Nisar; Suliman Alsaeed; Kanagaraj Muthuselvan; Baskar Sundaravadivoo; Kottakkaran Sooppy Nisar; Suliman Alsaeed

doi:10.3934/math.2023861

AIMS Mathematics

2023, Volume 8, Issue 7: 16846-16863. doi: 10.3934/math.2023861

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Discussion on iterative process of nonlocal controllability exploration for Hilfer neutral impulsive fractional integro-differential equation

1.
Department of Mathematics, Alagappa University, Karaikudi-630004, Tamil Nadu, India
2.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, 11942, Saudi Arabia
3.
School of Technology, Woxsen University-Hyderabad-502345, Telangana State, India
4.
Applied Sciences Collage, Department of Mathematical Sciences, Umm Al-Qura University P.O. Box 715, 21955, Makkah, Saudi Arabia
5.
Mathematics Department, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Saudi Arabia

Received: 12 February 2023 Revised: 14 April 2023 Accepted: 27 April 2023 Published: 15 May 2023
MSC : 34A08, 34A12, 34A37, 45J05, 93B05

This manuscript primarily focuses on the nonlocal controllability results of Hilfer neutral impulsive fractional integro-differential equations of order $ 0\leq w\leq1 $ and $ 0 < g < 1 $ in a Banach space. The outcomes are derived from the strongly continuous operator, Wright function, linear operator, and bounded operator. First, we explore the existence and uniqueness of the results of the mild solution of Hilfer's neutral impulsive fractional integro-differential equations using Schauder's fixed point theorem and an iterative process. In order to determine nonlocal controllability, the Banach fixed point technique is used. We employed some specific numerical computations and applications to examine the effectiveness of the results.
- Hilfer fractional derivative,
- nonlocal controllability,
- impulsive function,
- fixed point theorems,
- iterative process
Citation: Kanagaraj Muthuselvan, Baskar Sundaravadivoo, Kottakkaran Sooppy Nisar, Suliman Alsaeed. Discussion on iterative process of nonlocal controllability exploration for Hilfer neutral impulsive fractional integro-differential equation[J]. AIMS Mathematics, 2023, 8(7): 16846-16863. doi: 10.3934/math.2023861

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Abstract

This manuscript primarily focuses on the nonlocal controllability results of Hilfer neutral impulsive fractional integro-differential equations of order $ 0\leq w\leq1 $ and $ 0 < g < 1 $ in a Banach space. The outcomes are derived from the strongly continuous operator, Wright function, linear operator, and bounded operator. First, we explore the existence and uniqueness of the results of the mild solution of Hilfer's neutral impulsive fractional integro-differential equations using Schauder's fixed point theorem and an iterative process. In order to determine nonlocal controllability, the Banach fixed point technique is used. We employed some specific numerical computations and applications to examine the effectiveness of the results.

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