On a fractional differential inclusion with integral boundary conditions in Banach space

Authors: Phan Dinh Phung, Lê Xuân Trường,

https://doi.org/10.2478/s13540-013-0035-6

Publisher, magazine: ,

Publication year: 2013

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Abstract

We consider a class of boundary value problem in a separable Banach space E, involving a nonlinear differential inclusion of fractional order with integral boundary conditions, of the form $\left\{ Dαu(t)∈F(t,u(t),Dα−1u(t)),a.e.,t∈[0,1],Iβu(t)|t=0=0,u(1)=∫01u(t)dt, \right. $ ((*)) where D α is the standard Riemann-Liouville fractional derivative, F is a closed valued mapping. Under suitable conditions we prove that the solutions set of (*) is nonempty and is a retract in W α,1E(I). An application in control theory is also provided by using the Young measures.

Tags: fractional differential inclusion, boundary value problem, Green’s function, contractive set valued-map, retract, Young measures