Existence and multiplicity of positive solutions to a system of fractional difference equations with parameters

Abstract

Abstract We consider a fractional difference-sum boundary problem for a system of fractional difference equations with parameters. Using the Banach fixed point theorem, we prove the existence and uniqueness of solutions. We also prove the existence of at least one and two solutions by using the Krasnoselskii’s fixed point theorem for a cone map. Finally, we give some examples to illustrate our results.

Keywords

• Positive solution
• System of fractional difference equations
• Green’s function
• Cone