An Analysis Regarding to Approximate Controllability for Hilfer Fractional Neutral Evolution Hemivariational Inequality

• Published in: Qualitative theory of dynamical systems Vol. 21; no. 3
• Main Authors: Kavitha, K., Vijayakumar, V.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.09.2022; Springer Nature B.V
• Subjects: Controllability; Difference and Functional Equations; Dynamical Systems and Ergodic Theory; Evolution; Fixed points (mathematics); Fractional calculus; Inequalities; Mathematics; Mathematics and Statistics; Operators (mathematics); Probability density functions; Hemivariational inequality; 34K40; 34G10; Approximate controllability; Hilfer fractional derivative; Generalized Clarke’s subdifferential; Neutral systems; 93B05; 26A33; 34G25
• ISSN: 1575-5460; 1662-3592
• DOI: 10.1007/s12346-022-00611-z

The main motivation of our conversation is the approximate controllability of Hilfer fractional neutral evolution hemivariational inequalities. Using fractional calculus, the theory of operators semigroup and the probability density function, we first construct a new C 1 - β mild solution for Hilfer fractional differential inclusion. Secondly, we prove the approximate controllability of Hilfer fractional evolution hemivariational inequalities to linear and semilinear systems using characteristic solution operators and fundamental features via a fixed point theorem for multi-valued mappings. Finally, two examples are provided to demonstrate our theory.