We independently propose a new kind of the definition of fractional difference, fractional sum, and fractional difference equation, give some basic properties of fractional difference and fractional sum, and give some examples to demonstrate several methods of how to solve certain fractional difference equations.
Jin-Fa Cheng. Yu-Ming Chu. "Fractional Difference Equations with Real Variable." Abstr. Appl. Anal. 2012 (SI01) 1 - 24, 2012. https://doi.org/10.1155/2012/918529