EXISTENCE OF SOLUTIONS FOR NONLOCAL BOUNDARY VALUE PROBLEM OF FRACTIONAL DIFFERENTIAL EQUATIONS ON THE INFINITE INTERVAL

In this paper, we study a fractional differential equation;D;+u（t） + f(t, u（t）) = 0, t ∈（0, +∞）satisfying the boundary conditions:u′（0） = 0, limt→+∞;D;u（t） = g（u）,where 1 < α 2,;D;is the standard Caputo fractional derivative of orderα. The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O’Regan. Under a compactness criterion, the existence of solutions are established.