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Positive solution for a discrete fractional periodic boundary value problem. (English) Zbl 1268.26010

Summary: An existence criteria for a positive solution of the following discrete fractional periodic boundary value problem \[ \begin{aligned}(_{\alpha-1}\Delta^\alpha u)(t)&=\lambda u(t+\alpha-1)+f(t+\alpha-1,u(t+\alpha-1))\\ u(\alpha-1)&=u(\alpha-1+T),\end{aligned} \]
is established using a fixed point theorem for operators on cones. An example is included to illustrate our results.

MSC:

26A33 Fractional derivatives and integrals
39A05 General theory of difference equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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