Existence Of Solutions To Boundary Value Problems Of Fractional Difference Equations

In the thesis, first, we consider the existence of solutions to the following fractional difference boundary value problems where2＜v＜3,△v-3v is a fractional difference operator, N0,T={0,1,…, T}, We found the corresponding Green function by using the properties of the frac-tional sum, difference, the solution was given by using the Brouwer fixed point theorem and Banach’s contraction mapping principle when f is under given con-ditions. And we gave the difference between fractional-order difference equation and integer-order difference equation.Then, we consider the existence of solutions to the following fractional differ-ence boundary value problems where2＜v＜3,△v-3v is a fractional difference operator, N0,T={0,1,…,T}, we analysed the properties of Green function, So constructing a suitable space and cone and then establishing the existence of one positive solution or two positive solutions by use of Guo-Krasnoselskii fixed point theorem and the fixed point index theorem respectively.