On a Fractional Differential Inclusion in Banach Space Under Weak Compactness Condition
| Autor: | F. Z. Mostefai, C. Castaing, L. X. Truong, C. Godet-Thobie |
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| Rok vydání: | 2016 |
| Předmět: |
Pettis integral
021103 operations research Mathematical analysis 0211 other engineering and technologies Regular polygon Banach space Order (ring theory) 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Separable space Combinatorics Compact space Boundary value problem 0101 mathematics Fractional differential Mathematics |
| Zdroj: | Advances in Mathematical Economics Volume 20 ISBN: 9789811004759 |
| DOI: | 10.1007/978-981-10-0476-6_2 |
| Popis: | We consider a class of boundary value problem in a separable Banach space governed by a fractional differential inclusion with integral boundary conditions $$\displaystyle{\left \{\begin{array}{lll} w\text{-}D^{\alpha }u(t) \in F(t,u(t),w\text{-}D^{\alpha -1}u(t)), t \in [0,1] \\ I^{\beta }u(t)\vert _{t=0} = 0, u(1) =\int _{ 0}^{1}u(t)dt\end{array} \right.}$$ where α ∈ ]1, 2], \(\beta \in ]0,\infty [\) are given constant and w-D γ is the fractional w-R.L derivative of order γ ∈ {α − 1, α}, F is a convex weakly compact valued mapping. Topological properties of the solutions set are presented. Applications to control problems and further variants are provided. |
| Databáze: | OpenAIRE |
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