I.H. Kaddoura - Department of Mathematics, Lebanese International University, Saida, Lebanon
Sh.M. Al-Issa - Department of Mathematics, The International University of Beirut, Saida, Lebanon
H. Hamzae - Department of Mathematics, Lebanese International University, Saida, Lebanon

Here, we investigate the existence of solutions for the initial value problem of fractional-order differential inclusion containing a nonlocal infinite-point or Riemann–Stieltjes integral boundary conditions. A sufficient condition for the uniqueness of the solution is given. The continuous dependence of the solution on the set of selections and on some data is studied. At last, examples are designed to illustrate the applicability of the theoretical results.

Functional integro-differential inclusion, fixed point theorem, Riemann–Stieltjes integral boundary conditions, infinite-point boundary conditions