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Title
Fractional variable order differential equations with impulses: A study on the stability and existence properties
Type of Research Article
Keywords
impulsive condition; differential equations; fractional variable order; Ulam-Hyers stability; existence of solutions; fixed point theorem
Abstract
In this paper, for the first time, we study the existence and uniqueness of solutions of a Caputo variable-order initial value problem (IVP) in the impulsive settings. Our existence results are proved by using two fixed point theorems. The Ulam-Hyers stability of solutions is established for the variable order impulsive initial value problem. Finally, we provide an example to show the correctness of the results.
Researchers Amar Benkerrouche (First Researcher)، Sina Etemad (Second Researcher)، Mohammed Said Souid (Third Researcher)، Shahram Rezapour (Fourth Researcher)، Hijaz Ahmad (Fifth Researcher)، Thongchai Botmart (Not In First Six Researchers)