On a Multipoint Boundary Value Problem for a Fractional Order Differential Inclusion on an Infinite Interval

Abstract

We investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusion D(0+)(alpha)u(t) + F(t,u(t),u'(t)) (sic) 0, 0 < t < +infinity,u(0) = u'(0) = 0, D(alpha-1)u(+infinity) - Sigma(m-2)(i-1) beta(i)u(xi(i)) = 0, where D-0+(alpha) is the standard Riemann-Liouville fractional derivative, 2 < alpha < 3, 0 < xi(1) < xi(2) < center dot center dot center dot < xi(m-2) < +infinity, satisfies 0 < Sigma(m-2)(i=1) beta(i)xi(alpha-1)(i) < Gamma(alpha), and F : [0, +infinity) x R x R (sic) P(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.