Existence and rapid convergence results for nonlinear Caputo nabla fractional difference equations

Authors

Xiang Liu, Sun Yat-sen University
Baoguo Jia, Sun Yat-sen University
Lynn Erbe, University of Nebraska-LincolnFollow
Allan Peterson, University of Nebraska - LincolnFollow

Date of this Version

6-24-2017

Citation

2017, No. 51, 1–16; doi: 10.14232/ejqtde.2017.1.51 http://www.math.u-szeged.hu/ejqtde/

Abstract

This paper is concerned with finding properties of solutions to initial value problems for nonlinear Caputo nabla fractional difference equations. We obtain existence and rapid convergence results for such equations by use of Schauder’s fixed point theorem and the generalized quasi-linearization method, respectively. A numerical example is given to illustrate one of our rapid convergence results.