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Monotone iterative technique for fractional differential equations with periodic boundary conditions. (English) Zbl 1197.26007

Summary: 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.

MSC:

26A33 Fractional derivatives and integrals
34B99 Boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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