Special Session 13: Nonlinear differential and difference equations with applications to population dynamics

Solutions for a class of nonlinear fractional difference equations at resonance

Wenying Feng
Trent University
Canada
Co-Author(s):    H. Chen, Y. Cui, S. Kang, Y. Lu
Abstract:
We study a class of nonlinear fractional difference equations with nonlocal boundary conditions at resonance. The system is inspired by the three-point boundary value problem for differential equations that have been extensively studied. It is also an extension to a fractional difference equation arising from real-world applications. Applying the coincidence degree theory for semi-linear operators, we are able to obtain sufficient conditions for the existence of solutions. In addition, we prove a new property of the Gamma function and construct a family of examples to illustrate the applications of the results.