Existence of positive solution for some class of nonlinear fractional differential equations. (English) Zbl 1026.34008

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.


34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
26A33 Fractional derivatives and integrals
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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