Study of Hybrid Problems under Exponential Type Fractional-Order Derivatives

In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2024; pp. 1 - 9
Main Authors Abdo, Mohammed S., Idris, Sahar Ahmed, Albalwi, M. Daher, Idris, Tomadir Ahmed
Format Journal Article
LanguageEnglish
Published Cairo Wiley 29.05.2024
Hindawi Limited
Subjects
Boundary conditions
Boundary value problems
Differential equations
Fractional calculus
Green's functions
Integral equations
Laplace transforms
Operators (mathematics)
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Summary:In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional operator applied. In this regard, the corresponding hybrid fractional integral equation is obtained by the Caputo–Fabrizio operator’s properties with the Green function’s aid. Then, we apply Dhage’s nonlinear alternative to the Schaefer type to prove the existence results. Finally, two examples are provided to confirm the validity of our main results.
ISSN:2314-4629
2314-4785
DOI:10.1155/2024/2274198