Some novel existence and uniqueness results for the Hilfer fractional integro-differential equations with non-instantaneous impulsive multi-point boundary conditions and their application-Reference-Cited by-同舟云学术

Some novel existence and uniqueness results for the Hilfer fractional integro-differential equations with non-instantaneous impulsive multi-point boundary conditions and their application

Published:2023 Issue:2 Volume:8 Page:3469-3483
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Abdeljawad Thabet¹²,Mohammed Pshtiwan Othman³,Srivastava Hari Mohan⁴⁵⁶,Al-Sarairah Eman⁷⁸,Kashuri Artion⁹,Nonlaopon Kamsing¹⁰

Affiliation:

1. Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

2. Department of Medical Research, China Medical University, Taichung 40402, Taiwan

3. Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq

4. Department of Mathematics and Statistics, University of Victoria, BC V8W 3R4, Canada

5. Department of Mathematics and Informatics, Azerbaijan University, AZ1007 Baku, Azerbaijan

6. Center for Converging Humanities, Kyung Hee University, Dongdaemun-gu, Seoul 02447, Republic of Korea

7. Department of mathematics, Khalifa University, P.O. Box 127788, Abu Dhabi, United Arab Emirates

8. Department of mathematics, Al-Hussein Bin Talal University, P.O. Box 33011, Ma'an, Jordan

9. Department of Mathematics, Faculty of Technical and Natural Sciences, University "Ismail Qemali", 9400 Vlora, Albania

10. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Abstract

<abstract><p>In this article, we discuss conditions that are sufficient for the existence of solutions for some $ {\psi} $-Hilfer fractional integro-differential equations with non-instantaneous impulsive multi-point boundary conditions. By applying Krasnoselskii's and Banach's fixed point theorems, we investigate the existence and uniqueness of these solutions. Moreover, we have proved its boundedness of the method. We extend some earlier results by introducing and including the $ {\psi} $-Hilfer fractional derivative, nonlinear integral terms and non-instantaneous impulsive conditions. Finally, we offer an application to explain the consistency of our theoretical results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference46 articles.

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3. M. S. Abdo, S. K. Pancha, Fractional integro-differential equations involving ${\psi}$-Hilfer fractional derivative, Adv. Appl. Math. Mech., 11 (2019), 338–359. http://doi.org/10.4208/aamm.OA-2018-0143

4. M. R. Ali, A. R. Hadhoud, H. M. Srivastava, Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method, Adv. Differ. Equ., 2019 (2019), 115. https://doi.org/10.1186/s13662-019-2044-1

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