Existence of positive solutions in the space of Lipschitz functions to a class of fractional differential equations of arbitrary order. (English) Zbl 1425.34018
Summary: In this paper, we study sufficient conditions for the existence of positive solutions to a class of fractional differential equations of arbitrary order. Our solutions are placed in the space of Lipschitz functions and, perhaps, this is a part of the originality of the paper. For our study, we use a recent result about the relative compactness in Hölder spaces and the classical Schauder fixed point theorem.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 46N20 | Applications of functional analysis to differential and integral equations |
| 47N20 | Applications of operator theory to differential and integral equations |
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