Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions. (English) Zbl 1211.39002
Summary: We consider a discrete fractional boundary value problem of the form - , where is continuous, is a given functional, and . We give a representation for the solution to this problem. Finally, we prove the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem, the Brouwer theorem, and the Krasnosel’skii theorem.
|39A10||Additive difference equations|
|26A33||Fractional derivatives and integrals (real functions)|
|39A12||Discrete version of topics in analysis|