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Maximum principles for fractional differential equations derived from Mittag-Leffler functions. (English) Zbl 1202.34019

Summary: We present two new maximum principles for a linear fractional differential equation with initial or periodic boundary conditions. Some properties of the classical Mittag-Leffler functions are crucial in our arguments. These comparison results allow us to study the corresponding nonlinear fractional differential equations and to obtain approximate solutions.

MSC:

34A08 Fractional ordinary differential equations
34A30 Linear ordinary differential equations and systems
34B15 Nonlinear boundary value problems for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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