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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:
34A08Fractional differential equations
34A30Linear ODE and systems, general
34B15Nonlinear boundary value problems for ODE
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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