Modeling with fractional difference equations - ATICI, Ferhan M; SENGÜL, Sevgi (Journal of mathematical analysis and applications, 2010)
In this paper, we develop some basics of discrete fractional calculus such as Leibniz rule and summation by parts formula. We define simplest discrete fractional calculus of variations problem and derive Euler–Lagrange equation. We introduce and solve Gompertz fractional difference equation for tumor growth models.