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Article

Ahmad, Bashir ; Ntouyas, Sotiris
Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. (English). Mathematica Bohemica, vol. 139 (2014), issue 3, pp. 451-465
MSC: 34A08, 34A60, 34B10 | MR 3269368 | Zbl 06391465 | DOI: 10.21136/MB.2014.143936
Keywords:
differential inclusion; nonlocal condition; integral boundary condition; Leray Schauder alternative; fixed point theorem
Summary:
In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the multivalued map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative of Leray-Schauder type for single-valued maps with a selection theorem due to Bressan and Colombo, while in the third case we use a fixed point theorem for multivalued contractions due to Covitz and Nadler.
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