Initial value problems for fractional differential equations involving Riemann–Liouville sequential fractional derivative

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Abstract

In this paper, we shall discuss the properties of the well-known Mittag–Leffler function, and consider the existence and uniqueness of solution of the initial value problem for fractional differential equation involving Riemann–Liouville sequential fractional derivative by using monotone iterative method.

Keywords

Initial value problem
Fractional differential equation
Riemann–Liouville sequential fractional derivatives
Upper solution and lower solution

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Research supported by the NNSF-China (10971046) and the NSF of Shandong Province (ZR2009AM004).