Theoretical Results on Positive Solutions in Delta Riemann–Liouville Setting

Abstract

This article primarily focuses on examining the existence and uniqueness analysis of boundary fractional difference equations in a class of Riemann–Liouville operators. To this end, we firstly recall the general solution of the homogeneous fractional operator problem. Then, the Green function to the corresponding fractional boundary value problems will be reconstructed, and homogeneous boundary conditions are used to find the unknown constants. Next, the existence of solutions will be studied depending on the fixed-point theorems on the constructed Green’s function. The uniqueness of the problem is also derived via Lipschitz constant conditions.

Keywords

• Riemann–Liouville operators
• Green’s function (GF)
• fixed-point theorem
• existence and uniqueness solution