EXISTENCE OF SOLUTIONS OF A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION WITH FRACTIONAL DERIVATIVE AND FRACTIONAL INTEGRAL BOUNDARY CONDITIONS

This paper is concerned with the existence of solutions of the Fractional Boundary Value Problem {D(0)(p)z(t) + f(t, z(t)) = 0, t is an element of [0, 1] z(0) = z'(0) = 0, D(0)(q)z(1) + lambda I(0)(r)z(1) = 0 where D-0(p) is Riemann-Liouville fractional derivative of order p, I-0(r) denotes the Riemann- Lionville fractional integral of order r, p is an element of (2, 3], q is an element of (0, 1], r > 0, f : [0, 1]x R -> R be a continuous function and lambda not equal -Gamma(p + r)/Gamma(p - q). Some existence results are obtained by means of Krasnoselskii's Fixed Point Theorem and Banach Fixed Point Theorem.