Caputo-Hadamard fractional boundary-value problems in $ {\mathfrak{L}}^\mathfrak{p} $-spaces

Shayma Adil Murad; Ava Shafeeq Rafeeq; Thabet Abdeljawad; Shayma Adil Murad; Ava Shafeeq Rafeeq; Thabet Abdeljawad

doi:10.3934/math.2024849

AIMS Mathematics

2024, Volume 9, Issue 7: 17464-17488. doi: 10.3934/math.2024849

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Research article

Caputo-Hadamard fractional boundary-value problems in $ {\mathfrak{L}}^\mathfrak{p} $-spaces

1.
Department of Mathematics, College of Science, Univesity of Duhok, Duhok 42001, Iraq
2.
Department of Mathematics, College of Science, Univesity of Zakho, Duhok 42001, Iraq
3.
Department of Mathematics and Sciences, Prince Sultan Univesity, Riyadh 11586, Saudi Arabia
4.
Department of Medical Research, China Medical Univesity, Taichung 40402, Taiwan
5.
Department of Mathematics Kyung Hee Univesity, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
6.
Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences Uni., Ga-Rankuwa, South Africa

Received: 29 March 2024 Revised: 03 May 2024 Accepted: 10 May 2024 Published: 21 May 2024
MSC : 26A33, 34A08, 34D20, 34K20, 34B15, 34A12

The focal point of this investigation is the exploration of solutions for Caputo-Hadamard fractional differential equations with boundary conditions, and it follows the initial formulation of a model that is intended to address practical problems. The research emphasizes resolving the challenges associated with determining precise solutions across diverse scenarios. The application of the Burton-Kirk fixed-point theorem and the Kolmogorov compactness criterion in $ {\mathfrak{L}}^\mathfrak{p} $-spaces ensures the existence of the solution to our problem. Banach's theory is crucial for the establishment of solution uniqueness, and it is complemented by utilizing the Hölder inequality in integral analysis. Stability analyses from the Ulam-Hyers perspective provide key insights into the system's reliability. We have included practical examples, tables, and figures, thereby furnishing a comprehensive and multifaceted examination of the outcomes.
- Caputo-Hadamard fractional derivatives,
- Ulam-Hyers stability,
- Burton-Kirk fixed-point theorem,
- Hölder inequality,
- Kolmogorov compactness criterion
Citation: Shayma Adil Murad, Ava Shafeeq Rafeeq, Thabet Abdeljawad. Caputo-Hadamard fractional boundary-value problems in $ {\mathfrak{L}}^\mathfrak{p} $-spaces[J]. AIMS Mathematics, 2024, 9(7): 17464-17488. doi: 10.3934/math.2024849

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Abstract

The focal point of this investigation is the exploration of solutions for Caputo-Hadamard fractional differential equations with boundary conditions, and it follows the initial formulation of a model that is intended to address practical problems. The research emphasizes resolving the challenges associated with determining precise solutions across diverse scenarios. The application of the Burton-Kirk fixed-point theorem and the Kolmogorov compactness criterion in $ {\mathfrak{L}}^\mathfrak{p} $-spaces ensures the existence of the solution to our problem. Banach's theory is crucial for the establishment of solution uniqueness, and it is complemented by utilizing the Hölder inequality in integral analysis. Stability analyses from the Ulam-Hyers perspective provide key insights into the system's reliability. We have included practical examples, tables, and figures, thereby furnishing a comprehensive and multifaceted examination of the outcomes.

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