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RESEARCH ARTICLE

Investigate the solution of an initial Hilfer fractional value problem

Amol D. Khandagale1 ,  Arif S. Bagwan2 ,  Sabri T. M. Thabet3,4,5* ,  Imed Kedim6
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1 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Chhatrapati, Sambhajinagar, India
2 Department of Applied Sciences Humanities, Pimpri Chinchwad College of Engineering, Nigdi, Pune, India
3 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu, India
4 Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen
5 Department of Mathematics, College of Science, Korea University, Seongbuk-gu, Seoul, Republic of Korea
6 Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
IJOCTA, 025120056 https://doi.org/10.36922/IJOCTA025120056
Received: 20 March 2025 | Revised: 10 May 2025 | Accepted: 13 May 2025 | Published online: 3 June 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This paper aims to investigate sufficient criteria of the existence solution for a new category of nonlinear fractional differential equation under the Hilfer fractional derivative. The primary existence results are achieved by using a modified version of the Krasnoselskii-Dhage fixed-point theorem in the weighted Banach space. Finally, an application is illustrated to test the validity of the findings.

Keywords
Initial value problem
Hilfer fractional derivative
Fixed point theorem
Funding
None.
Conflict of interest
The authors declare no conflict of interest.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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