Fractional Order of Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator

Abstract

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented.

Keywords

• fractional differential inclusion
• maximal monotone operator
• Riemann–Liouville integral
• absolutely continuous in variation
• Vladimirov pseudo-distance