ON THE EXISTENCE AND UNIQUENESS OF SOLUTION FOR A CLASS OF FRACTIONAL ORDER BOUNDARY VALUE PROBLEMS

In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. Schauder s fixed point Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution.