Opuscula Math. 29, no. 3 (2009), 289-304
Monotone iterative technique for fractional differential equations with periodic boundary conditions
J. D. Ramírez
A. S. Vatsala
Abstract. In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.
Keywords: Riemann-Liouville fractional derivative, monotone method, periodic boundary value problem.
Mathematics Subject Classification: 26A33, 34B99, 34C25.