Multiple Solutions to Fractional Difference Boundary Value Problems

Abstract EN

The following fractional difference boundary value problems ▵νyt=-ft+ν-1,yt+ν-1, y(ν-2)=y(ν+b+1)=0 are considered, where 1<ν≤2 is a real number and ▵νy(t) is the standard Riemann-Liouville fractional difference.

Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions on f which are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively.

Our results significantly improve and generalize those in the literature.

A number of examples are given to illustrate our main results.