New results on approximate controllability of fractional delay integrodifferential systems of order 1 < r < 2 with Sobolev-type

Abstract

In this manuscript, we look at fractional evolution integrodifferential systems with infinite delay of order r∈(1,2) with control problems. To begin, we establish the mild solution for the given system. Further, we look at the approximate controllability outcomes utilizing multivalued functions, Sobolev-type, nonlocal circumstances, fractional analysis, fixed point technique, and cosine families. Finally, an application for generating the primary outcome theory has been created.

Keywords

• Fractional derivatives and integrals
• Fixed point techniques
• Sobolev-type
• Cosine families
• Mild solutions