Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system

Hasib Khan, Aziz Khan, Fahd Jarad and Anwar Shah

Chaos, Solitons & Fractals, 2020, vol. 131, issue C

Abstract: The study of existence of solution ensures the essential conditions required for a solution. Keeping the importance of the study, we initiate the existence, uniqueness and data dependence of solutions an Atangana-Baleanu-Caputo (ABC)-fractional order differential impulsive system. For this purpose, the suggested ABC-fractional order differential impulsive system is transferred into equivalent fixed point problem via integral operator. The operator is then analyzed for boundedness, continuity and equicontinuity. Then Arzela-Ascolli theorem ensures the relatively compactness of the operator and the Schauder’s fixed point theorem and Banach’s fixed point theorem are utilized for the existence and uniqueness of solution. Data dependence and expressive application are also provided.

Keywords: ABC-fractional order impulsive system; Existence and uniqueness of solution; Data dependence (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304230

DOI: 10.1016/j.chaos.2019.109477

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