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

• Datum: 1999
• Hauptverfasser: Vityuk, A. N., Вітюк, А. Н.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 1999
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4757
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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...