Abstract
We prove a theorem on the existence of solutions of the differential inclusion\(D_0^\alpha u(x) \in F(x,u(x)), u_{1 - \alpha } (0) = \gamma , \left( {u_{1 - \alpha } (x) = 1_0^{1 - \alpha } u(x)} \right),\) where\(\alpha \in (0,1), D_0^\alpha u(x) \left( {1_0^{1 - \alpha } u(x)} \right)\) is the Riemann-Liouville derivative (integral) of order α, and the multivalued mappingF(x, u) is upper semicontinuous inu.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1562–1565, November, 1999.
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Vityuk, A.N. On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side. Ukr Math J 51, 1764–1768 (1999). https://doi.org/10.1007/BF02525261
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DOI: https://doi.org/10.1007/BF02525261