On a new structure of multi-term Hilfer fractional impulsive neutral Levin-Nohel integrodifferential system with variable time delay

Thabet Abdeljawad; Sabri T. M. Thabet; Imed Kedim; Miguel Vivas-Cortez; Thabet Abdeljawad; Sabri T. M. Thabet; Imed Kedim; Miguel Vivas-Cortez

doi:10.3934/math.2024357

AIMS Mathematics

2024, Volume 9, Issue 3: 7372-7395. doi: 10.3934/math.2024357

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Research article

On a new structure of multi-term Hilfer fractional impulsive neutral Levin-Nohel integrodifferential system with variable time delay

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, Kyung Hee University 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea
4.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa 0204, South Africa
5.
Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen
6.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
7.
Escuela de Ciencias Fisicas y Matematicas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Catolica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador

Received: 02 January 2024 Revised: 22 January 2024 Accepted: 29 January 2024 Published: 20 February 2024
MSC : 34A08, 34A37, 34D20, 35A23

The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-Mittag-Leffler (UHML) stability is studied by utilizing the generalized Gronwall's inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville ($ \mathcal{R.L.} $) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings.
- Hilfer fractional derivatives,
- Leivn-Nohel equation,
- Ulam-Hyers-Mittag-Leffler stability,
- impulsive condition,
- generalized Gronwall's inequality
Citation: Thabet Abdeljawad, Sabri T. M. Thabet, Imed Kedim, Miguel Vivas-Cortez. On a new structure of multi-term Hilfer fractional impulsive neutral Levin-Nohel integrodifferential system with variable time delay[J]. AIMS Mathematics, 2024, 9(3): 7372-7395. doi: 10.3934/math.2024357

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Abstract

The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-Mittag-Leffler (UHML) stability is studied by utilizing the generalized Gronwall's inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville ($ \mathcal{R.L.} $) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings.

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