EXISTENCE RESULT OF POSITIVE SOLUTION FOR BOUNDARY VALUE PROBLEMS OF FRACTIONAL ORDER WITH INTEGRO-DIFFERENTIAL BOUNDARY CONDITIONS

In this paper we study the following fractional boundary value problem with integrodifferential boundary conditions D-0(alpha)+u(t) - f(t,u(t),D-0+(alpha-1) u(t),D-0+(1-alpha) u(t)) = 0, t epsilon [0,T], n - 1 <= alpha < n, { u((j)) (0) -0, D-0+(alpha-1) u(T) + integral(T)(0) u(omega)d omega + Sigma(m 2)(i=1) beta(i)u(xi(i)) - 0, j -0,...,n-2, 0 < xi(i) < xi(i+1) < T, beta(i) epsilon [0,infinity), i - 1,2,...1m - 2, n epsilon N \ {1}, T > 0, where D-0+(alpha), D-0+(alpha-1) represent the standard Riemann-Liouville fractional derivative of order a. Themain result includes some interesting fixed point and functional analysis techniques to obtain claimed existence result.