HIGHER ORDER NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, we study the method of upper and lower so- lutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differ- ential equations of the type c D q 0+u(t) + f(t, u(t)) = 0, t 2 (0,1) u ' (0) = u ' (�), u '' (0) = 0, u ''' (0) = 0,...,u (n−1) (0) = 0, u(1) = �u(�), where, n 1 < q < n, n(� 3) 2 N, 0 < �, ,� < 1 and c D q is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.