On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side - Vityuk, A. N. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
We prove a theorem on the existence of solutions of the differential inclusion \(D_0^α u(x) F(x,u(x)), u_1 - α (0) = γ , ( u_1 - α (x) = 1_0^1 - α u(x) ),\) where \(α (0,1), D_0^α u(x) ( 1_0^1 - α u(x) )\) is the Riemann-Liouville derivative (integral) of order α, and the multivalued mappingF(x, u) is upper semicontinuous inu.