On the existence and uniqueness of solution for a class of fractional order boundary value problemsAzizollah Babakhani (pp. 50-58)
In this paper, we discuss existence and uniqueness of solutions to nonlinear frac- tional order ordinary di®erential 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. Schauders 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.
fractional differential equations, integral boundary conditions, gamma function, Banach space, completely continuous operator, existence results.