2019
Том 71
№ 8

On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side

Vityuk A. N.

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.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 11, pp 1764-1768.

Citation Example: Vityuk A. N. On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side // Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1562–1565.

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