Maximum and Minimum Results for the Green’s Functions in Delta Fractional Difference Settings

Abstract

The present paper is dedicated to the examination of maximum and minimum results based on Green’s functions via delta fractional differences for a class of fractional boundary problems. For such a purpose, we built the corresponding Green’s functions based on the falling factorial functions. In addition, using the constructed Green’s function, the positivity of the function and its corresponding delta function are presented. We also verified the occurrence of two distinct functions with the same Green’s function. The maximality and minimality of the Green’s function show a good qualitative agreement. Finally, we considered some special examples to explain the obtained results.

Keywords

• Riemann–Liouville operators
• Green’s functions
• positivity results
• max and min results