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Zbl 1026.34008
Zhang, Shuqin
Existence of positive solution for some class of nonlinear fractional differential equations. (English)
[J] J. Math. Anal. Appl. 278, No.1, 136-148 (2003). ISSN 0022-247X

The author considers nonlinear differential equations involving a generalised fractional differential operator corresponding to a generalised Riemann-Liouville fractional integral. He focuses on questions of existence and uniqueness of positive solutions to the equations. In the first two sections of the paper, the author introduces the definitions used, and gives basic theory. In Section 3, he gives a sequence of existence and uniqueness results followed by several lemmas and theorems that guarantee, under suitable conditions, the existence of multiple (infinite sequences of) positive solutions.
[Neville Ford (Chester)]

MSC 2000:: *34A25 Analytical theory of ODE
26A33 Fractional derivatives and integrals (real functions)
34A12 Initial value problems for ODE
34A34 Nonlinear ODE and systems, general

Keywords: fractional differential equations; positive solutions

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