Multiterm Impulsive Caputo–Hadamard Type Differential Equations of Fractional Variable Order

Date
2022-11-10
Authors
Benkerrouche, Amar
Souid, Mohammed Said
Stamov, Gani
Stamova, Ivanka
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Journal ISSN
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Abstract

In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established in the form of two fixed point theorems. In addition, Ulam–Hyers stability sufficient conditions are proved illustrating the suitability of the derived fundamental results. The obtained results are supported also by an example. Finally, the conclusion notes are highlighted.

Description
Keywords
Caputo-Hadamard fractional derivative, variable order, impulses, existence of solutions, uniqueness, fixed point theorem, Ulam-Hyers stability
Citation
Axioms 11 (11): 634 (2022)
Department
Mathematics