A Study of Monotonicity Analysis for the Delta and Nabla Discrete Fractional Operators of the Liouville–Caputo Family

Abstract

In the present article, we explore the correlation between the sign of a Liouville–Caputo-type difference operator and the monotone behavior of the function upon which the difference operator acts. Finally, an example is also provided to demonstrate the application and the validation of the results which we have proved herein.

Keywords

• delta and nabla discrete fractional operators
• Liouville–Caputo fractional difference operators
• positivity analysis
• monotonicity analysis