Existence Theorems for Hybrid Fractional Differential Equations with ψ-Weighted Caputo–Fabrizio Derivatives

In this study, two classes of hybrid boundary value problems involving ψ-weighted Caputo–Fabrizio fractional derivatives are considered. Based on the properties of the given operator, we construct the hybrid fractional integral equations corresponding to the hybrid fractional differential equations....

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2023; pp. 1 - 13
Main Authors Alshammari, Mohammad, Alshammari, Saleh, Abdo, Mohammed S.
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2023
Hindawi Limited
Subjects
Boundary value problems
Continuity (mathematics)
Derivatives
Differential equations
Dynamical systems
Existence theorems
Fixed points (mathematics)
Fractional calculus
Integral equations
Laplace transforms
Mathematical analysis
Mathematics
Operators (mathematics)
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Summary:In this study, two classes of hybrid boundary value problems involving ψ-weighted Caputo–Fabrizio fractional derivatives are considered. Based on the properties of the given operator, we construct the hybrid fractional integral equations corresponding to the hybrid fractional differential equations. Then, we establish and extend the existence theory for given problems in the class of continuous functions by Dhage’s fixed point theory. Furthermore, as special cases, we offer further analogous and comparable conclusions. Finally, we give two examples as applications to illustrate and validate the results.
ISSN:2314-4629
2314-4785
DOI:10.1155/2023/8843470