Existence And Uniqueness For Several Classes Of Boundary Value Problems For Fractional Difference Equations

Two types of fractional boundary value problems will be discussed in thispaper. By using some fxed point theorems and contraction principle, we ob-tain sufcient conditions for the existence and uniqueness of solutions to theseproblems.In frst chapter, we discussed corresponding historical background,researchstatus. We also introduced some defnitions and lemmas for necessary.In second chapter,we analyze a discrete fractional boundary value prob-lem of the form Δαy(t)=f (t+α1, y(t+α1)), ay(0)+by(T+1)=c,where t∈N1T+α1α,0<α≤1, f: N0T×Xâ†'X is continuous. We givea equivalent form to this problem. We then obtain sufcient conditions forthe existence and uniqueness of solution to this problem by using some fxedpoint theorems.In third chapter, we discuss the boundary value problem of fractional dif-ference equations with fractional boundary value condition. We construct anddeduce Green’s function for this problem and derive it’s properties. By meansof some fxed point theorems, existence and uniqueness results of solutions areobtained.