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.
Highlights
In recent decades, fractional equations and inclusions have proven to be interesting tools in the modeling of many physical or economic phenomena
The main objective of the present work is to develop the existence theory for a coupled system of evolution inclusion driven by fractional differential equation and time and state dependent maximal monotone operators
We investigate a second order problem governed a time and state dependent maximal monotone operator with Lipschitz perturbation in a separable Hilbert space E (The second order is in the state variable x)
Summary
Fractional equations and inclusions have proven to be interesting tools in the modeling of many physical or economic phenomena. The main objective of the present work is to develop the existence theory for a coupled system of evolution inclusion driven by fractional differential equation and time and state dependent maximal monotone operators. −u(t) ∈ A t,x (t) u ( t ) + f ( t, x ( t ), u ( t )) a.e. Secondly, we investigate a class of fractional order problem driven by a time and state dependent maximal monotone operator with Lipschitz perturbation in E of the form. Within the framework of studies concerning coupled systems of evolution inclusion driven by fractional differential equation and time and state dependent maximal monotone operator, our results are fairly general and new and give further insight into the characteristics of both evolution inclusion and fractional order boundary value problems
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