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

• Date: 1999
• Main Authors: Vityuk, A. N., Вітюк, А. Н.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1999
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4757
• Journal Title: 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...