Results on controllability for Sobolev type fractional differential equations of order 1<r<2 with finite delay

Abstract

In this article, exact controllability results for Sobolev fractional delay differential system of 1<r<2 are investigated. Fractional analysis, cosine and sine function operators, and Schauder's fixed point theorem are applied to verify the main results of this study. To begin, we use sufficient conditions to explore the controllability for fractional evolution differential system with finite delay. Lastly, an example is provided to illustrate the obtained theoretical results.

Keywords

• fractional differential systems
• controllability
• mainardi's wright-type function
• sobolev type
• mild solutions