Existence results for a system of sequential differential equations with varying fractional orders via Hilfer-Hadamard sense

Muath Awadalla; Manigandan Murugesan; Subramanian Muthaiah; Bundit Unyong; Ria H Egami; Muath Awadalla; Manigandan Murugesan; Subramanian Muthaiah; Bundit Unyong; Ria H Egami

doi:10.3934/math.2024486

AIMS Mathematics

2024, Volume 9, Issue 4: 9926-9950. doi: 10.3934/math.2024486

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Existence results for a system of sequential differential equations with varying fractional orders via Hilfer-Hadamard sense

1.
Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia
2.
Center for Computational Modeling, Chennai Institute of Technology, Chennai, 600069, Tamil Nadu, India
3.
Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, 641407, Tamilnadu, India
4.
Department of Mathematics and Statistics, Center of Excellence for Ecoinformatics, School of Science, Walailak University, Nakhon Si Thammarat 80160, Thailand
5.
Department of Mathematics, College of Science and Humanities in Sulail, Prince Sattam Bin Abdulaziz University, Saudi Arabia

Received: 20 January 2024 Revised: 24 February 2024 Accepted: 05 March 2024 Published: 12 March 2024
MSC : 34A08, 34B15, 45G15

We investigate the criteria for both the existence and uniqueness of solutions within a nonlinear coupled system of Hilfer-Hadamard sequential fractional differential equations featuring varying orders. This system is complemented by nonlocal coupled Hadamard fractional integral boundary conditions. The desired outcomes are attained through the application of well-established fixed-point theorems. It is underscored that the fixed-point approach serves as an effective method for establishing both the existence and uniqueness of solutions to boundary value problems. The results obtained are further demonstrated and validated through illustrative examples.
- Hilfer-Hadamard derivatives,
- sequential derivatives,
- Hadamard integrals,
- existence,
- uniqueness,
- fixed point
Citation: Muath Awadalla, Manigandan Murugesan, Subramanian Muthaiah, Bundit Unyong, Ria H Egami. Existence results for a system of sequential differential equations with varying fractional orders via Hilfer-Hadamard sense[J]. AIMS Mathematics, 2024, 9(4): 9926-9950. doi: 10.3934/math.2024486

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Abstract

We investigate the criteria for both the existence and uniqueness of solutions within a nonlinear coupled system of Hilfer-Hadamard sequential fractional differential equations featuring varying orders. This system is complemented by nonlocal coupled Hadamard fractional integral boundary conditions. The desired outcomes are attained through the application of well-established fixed-point theorems. It is underscored that the fixed-point approach serves as an effective method for establishing both the existence and uniqueness of solutions to boundary value problems. The results obtained are further demonstrated and validated through illustrative examples.

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