Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay. (November 2019) - Aimene, D.; Baleanu, D.; Seba, D.
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.