Abstract
We investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusionD0+αut+Ft,ut,u′t∋0,0<t<+∞,u0=u′0=0,Dα-1u+∞-∑i=1m-2βiuξi=0, whereD0+αis the standard Riemann-Liouville fractional derivative,2<α<3,0<ξ1<ξ2<⋯<ξm-2<+∞, satisfies0<∑i=1m-2βiξiα-1<Γ(α), and F:[0,+∞)×ℝ×ℝ→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.
Highlights
We investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusion D0α+ u(t) + F(t, u(t), u(t)) ∋ 0, 0 < t < +∞, u(0) = u(0) = 0, Dα−1u(+∞) − ∑mi=−12 βiu(ξi) = 0, where D0α+ is the standard Riemann-Liouville fractional derivative, 2 < α < 3, 0 < ξ1 < ξ2 < ⋅ ⋅ ⋅ < ξm−2 < +∞, satisfies 0 < ∑mi=−12 βiξiα−1 < Γ(α), and F : [0, +∞) × R × R → P(R) is a set-valued map
We will consider the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusion
Fractional differential equations have been of great interest recently
Summary
We will consider the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusion. The existence of solutions of initial value problems for fractional order differential equations has been studied in the literature [5,6,7,8,9,10,11,12,13,14,15,16,17] and the references therein. Several qualitative results for fractional differential inclusions were obtained in [19,20,21,22,23] and the references therein. In the first result (Theorem 21), we consider the case when the right hand side has convex values and prove an existence result via nonlinear alternative for Kakutani maps.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
