Existence of Solutions for a Hadamard Fractional Boundary Value Problem at Resonance

We explore the existence of solutions for a Hadamard fractional differential equation, subject to nonlocal boundary conditions, which contain Hadamard fractional derivatives and Riemann–Stieltjes integrals. This problem is a resonant one in the sense that the corresponding homogeneous boundary-value...

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Published inFractal and fractional Vol. 9; no. 2; p. 119
Main Authors Luca, Rodica, Tudorache, Alexandru
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2025
Subjects
Boundary conditions
Boundary value problems
Calculus
Differential equations
existence
Fractional calculus
Hadamard fractional differential equation
High-definition television
Integrals
nonlocal boundary conditions
resonant problem
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ISSN2504-3110
2504-3110
DOI10.3390/fractalfract9020119

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Abstract We explore the existence of solutions for a Hadamard fractional differential equation, subject to nonlocal boundary conditions, which contain Hadamard fractional derivatives and Riemann–Stieltjes integrals. This problem is a resonant one in the sense that the corresponding homogeneous boundary-value problem has nontrivial solutions. In the proof of the main result, we use the Mawhin continuation theorem.
AbstractList We explore the existence of solutions for a Hadamard fractional differential equation, subject to nonlocal boundary conditions, which contain Hadamard fractional derivatives and Riemann–Stieltjes integrals. This problem is a resonant one in the sense that the corresponding homogeneous boundary-value problem has nontrivial solutions. In the proof of the main result, we use the Mawhin continuation theorem.
Audience Academic
Author Luca, Rodica
Tudorache, Alexandru
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Copyright COPYRIGHT 2025 MDPI AG
2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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– notice: 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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SubjectTerms Boundary conditions
Boundary value problems
Calculus
Differential equations
existence
Fractional calculus
Hadamard fractional differential equation
High-definition television
Integrals
nonlocal boundary conditions
resonant problem
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Title Existence of Solutions for a Hadamard Fractional Boundary Value Problem at Resonance
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