On a multipoint boundary value problem for a fractional order differential inclusion on an infinite interval
Summary: We investigate the existence of solutions for the multipoint boundary value problem of a fractional-order differential inclusion \[ \begin{aligned} & D^\alpha_{0^+}u(t) + F(t, u(t), u'(t)) \ni 0,\quad 0 < t < +\infty,\\ & u(0) = u'(0) = 0, D^{\alpha - 1}u(+\infty) - \sum^{m-2}_{i=1} \beta_i u(\xi_i) = 0\end{aligned}, \] where \(D^\alpha_{0^+}\) is the standard Riemann-Liouville fractional derivative, \(2 < \alpha < 3\), \(0 < \xi_1 < \xi_2 < \dotsb < \xi_{m-2} < +\infty\), \(0 < \sum^{m-2}_{i=1} \beta_i \xi^{\alpha - 1}_i < \Gamma(\alpha)\), and \(F : [0, +\infty) \times \mathbb R \times \mathbb R \to \mathcal P(\mathbb R)\) is a set-valued map. Several results are obtained by using suitable fixed point theorems when the right-hand-side has convex or nonconvex values.
scientific article; zbMATH DE number 6171645
scientific article