Results on the existence and controllability of fractional integro-differential system of order 1 < r < 2 via measure of noncompactness

This manuscript is mainly focusing on the existence and controllability of fractional integro-differential system of order 1 < r < 2 with infinite delay. Our article's principal findings proved based on the theoretical concepts related to the fractional calculus and the measure of noncompactness. Firstly, we prove the existence of mild solution for the fractional evolution system and continue to discuss the system's exact controllability. Then, we extend our results to the concept of nonlocal conditions. Lastly, we provide theoretical and practical applications to assist in the effectiveness of the discussion. (C) 2020 Elsevier Ltd. All rights reserved.