Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay. (November 2019)

• Record Type: Journal Article
• Authors: Aimene, D.; Baleanu, D.; Seba, D.
• Is Part Of: Chaos, solitons and fractals. Volume 128(2019)
• Page Start: 51
• Page End: 57
• Publication Date: 2019-11
• Subjects: Fractional derivatives and integrals -- Controllability -- Differential equations with impulses -- Semigroup and fixed-point theories; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.07.027
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Establishing a relationship between Atangana-Baleanu-Caputo derivative and semilinear systems. Extend the principle of application of the control function on different type of fractional systems. Prove the existence of mild solutions by adopting Darbo's fixed point techniques. Show the effect of impulses and delay on fractional differential equations with an Atangana-Baleanu-Caputo derivative. Build a study on delay systems by establishing some spaces. Abstract: We discuss the controllability of semilinear differential equations of fractional order with impulses and delay. We make use of the Atangana-Baleanu derivative. Our main tools are semigroup theory, the fixed point theorem due to Darbo and their combination with the properties of measures of noncompactness. Our abstract results are well supported by an illustrative example.