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Positive solutions for a class of boundary value problems with fractional \(q\)-differences. (English) Zbl 1216.39013

From the introduction: The question of the existence of positive solutions for fractional \(q\)-difference boundary value problems is in its infancy, being available in the literature in only one paper on the subject considering Dirichlet type boundary conditions. As is well-known, the aim of finding positive solutions to boundary value problems is of main importance in various fields of applied mathematics. In addition, since \(q\)-calculus has a tremendous potential for applications, we find it pertinent to investigate such a demand.
This paper is organized as follows: in Section 2 we introduce some notation and provide to the reader the definitions of the \(q\)-fractional integral and differential operators together with some basic properties. In Section 3, sufficient conditions for the existence of positive solutions for a class of boundary value problems are given, and finally an example is provided.

MSC:

39A13 Difference equations, scaling (\(q\)-differences)
39A12 Discrete version of topics in analysis
34A08 Fractional ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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