J. Nonl. Evol. Equ. Appl. 2021 (7), pp. 137-151, published on February 19, 2022:

Some results on controllability and optimal controls for a fractional non-autonomous system with a deviated argument

A. Raheem, M. Kumar

Department of Mathematics, Aligarh Muslim University, Aligarh - 202002, India.

Received on September 22, 2020, revised version on November 17, 2021
Accepted on February 13, 2021

Communicated by Gasston M. N'Guérékata

Abstract.  In this paper, we are concerned with a non integer order non autonomous system with a deviated argument. Existence and uniqueness of mildsolution and controllability of the problem are proved by using the concept of measure of non compactness and Mönch's fixed point theorem. Further, we studied the optimal controllability of the problem. In the last section, results are validated by an example.
Keywords:controllability; optimal control; fractional non autonomous system, deviated argument, measure of non compactness; Mönch’s condition..
2010 Mathematics Subject Classification:   93B05, 93C23, 34A08, 47H08.

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