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.


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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