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Wang, Changyou; Zhang, Haiqiang; Wang, Shu

Positive solution of a nonlinear fractional differential equation involving Caputo derivative. (English) Zbl 1248.34006

Discrete Dyn. Nat. Soc. 2012, Article ID 425408, 16 p. (2012).
Summary: We are concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained.

Cited in 8 Documents

MSC:

34A08 Fractional ordinary differential equations

Keywords:

nonlinear fractional differential equation; Caputo derivatives
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\textit{C. Wang} et al., Discrete Dyn. Nat. Soc. 2012, Article ID 425408, 16 p. (2012; Zbl 1248.34006)
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References:

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