Several Classes Of Boundary Value Problems For Fractional Difference Equations

This paper is concerned with the existence and uniqueness of positive solution to a fractional difference equation with nonlocal conditions, and the existence of positive solution to a discrete fractional multi-point boundary value problem with fractional boundary value conditions.In chapter 2, we analyze a fractional difference equation with nonlocal condi-tions of the form â–³vy(t)= f(t+v-1, y(t+v-1)), y(v-2)= 0, y(v+b)= g(y), where t E N0b,1<v≤2, f:N(v-2)(v+b)×Râ†' R is continuous. We then discuss the existence and uniqueness of positive solution to this problem by using fixed point theorem.In chapter 3, we discuss the existence of positive solution to a discrete fractional multi-point boundary value problem with fractional boundary value conditions. Bas-ing on Green’s function and its properties, we analyze existence results of positive solutions by means of fixed point theorem.