Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses

Assia Boudjerida and Djamila Seba

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

Abstract: This paper deals with the approximate controllability of a class of non-instantaneous impulsive hybrid systems for fractional differential inclusions under Hilfer derivative of order 1<σ<2 and type 0≤ζ≤1, on weighted spaces. As an alternative to the Wright function which is defined only when 0<σ<1, we make use of a family of general fractional resolvent operators to give a proper form of the mild solution. This latter is consequently formulated by Laplace transform, improving and extending important results on this topic. Based on known facts about fractional calculus and set-valued maps, properties of the resolvent operator, and a hybrid fixed point theorem for three operators of Schaefer type, the existence result and the approximate controllability of our system is achieved. An example is given to demonstrate the effectiveness of our result.

Keywords: Hybrid systems; Fractional differential inclusions; Approximate controllability; Non-instantaneous impulses; Hilfer fractional derivative; Resolvent operators; Mild solutions (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004793

DOI: 10.1016/j.chaos.2021.111125

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