Controllability of Nonlocal Impulsive Semilinear Differential Inclusions with Fractional Sectorial Operators and Infinite Delay

This paper demonstrates the controllability of two fractional nonlocal impulsive semilinear differential inclusions with infinite delay, where the linear part is a fractional sectorial operator and the nonlinear term is a multivalued function. The operator families generated by the linear part are not assumed to be compact. The objective is achieved using the properties of fractional sectorial operators and the Hausdorff measure of noncompactness. The results generalise several recent findings, and the method can be used to extend further contributions to cases where the linear term is a fractional sectorial operator and the nonlinear term is a multivalued function, in the presence of instantaneous impulses and infinite delays. The novelty of this work lies in initiating the study of the controllability of a system involving a fractional Caputo derivative under infinite impulses and delays. An example is presented to verify the theoretical developments. Given the wide-ranging applications of fractional calculus in medicine, energy and other scientific fields, this work contributes to those domains. KEYWORDS Caputo derivative, mazur's lemma, mild solutions, multivalued functions, noncompact measure, phase space