Special Session 13: Nonlinear differential and difference equations with applications to population dynamics
Monotonicity and Convexity for Discrete Fractional Operators with Applications to Fractional Difference Equations
Christopher S. GOODRICH
School of Mathematics and Statistics, Sydney, UNSW USA
Co-Author(s):
Abstract:
I will discuss the connections between the sign of a discrete fractional operator evaluated at a point $n$, such as
$$\big(\Delta^{\beta}\circ\Delta^{\alpha}u\big)(n),$$
and the monotonicity and convexity of the function $u$. Some representative results in the area will be discussed. Applications to the analysis of fractional difference equations will be mentioned.