Approximate Controllability for Sobolev-Type Fuzzy Hilfer Fractional Neutral Integro-Differential Inclusion with Clarke Subdifferential Type
摘要
This paper focuses on the approximate controllability of Sobolev-type fuzzy Hilfer fractional neutral integro-differential inclusions involving the Clarke subdifferential. We establish the approximate controllability of this inclusion problem using fuzzy set theory, Sobolev-type methods, Fractional calculus, and Clarke subdifferentials. These techniques help to derive the necessary conditions for approximate controllability of the system. Dhage’s fixed point theorem is applied to prove the results related to approximate controllability. Finally, an example is provided to illustrate the discussion.