In this paper, we apply the fractional calculus and a suitable fixed point theorem with the measure of noncompactness to give the sufficient conditions of the controllability for a new class of fractional neutral integro-differential evolution systems with infinite delay and nonlocal conditions. The results are obtained here under some weakly noncompactness conditions. Thus they improve and generalize many well-known results. At the end of this paper, two examples are given to explain our abstract conclusions.

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This paper investigates a fractional-order linear system in the frame of Atangana–Baleanu fractional derivative. First, we prove that some properties for the Caputo fractional derivative also hold in the sense of AB fractional derivative. Subsequently, several sufficient criteria to guarantee the finite-time stability and the finite-time boundedness for the system are derived. Finally, an example is presented to illustrate the validity of our main results.

This paper studies the finite-time stability of fractional singular time-delay systems. First, by the method of the steps, we discuss the existence and uniqueness of the solutions for the equivalent systems to the fractional singular time-delay systems. Furthermore, we give the Mittag-Leffler estimation of the solutions for the equivalent systems and obtain the sufficient conditions of the finite-time stability for the original systems. MSC: 34K20

The exact controllability results for Hilfer fractional differential inclusions involving nonlocal initial conditions are presented and proved. By means of the multivalued analysis, measure of noncompactness method, fractional calculus combined with the generalized Monch fixed point theorem, we derive some sufficient conditions to ensure the controllability for the nonlocal Hilfer fractional differential system. The results are new and generalize the existing results. Finally, we talk about an example to interpret the applications of our abstract results.