CONVERGENCE OF APPROXIMATE SOLUTIONS TO NONLINEAR CAPUTO NABLA FRACTIONAL DIFFERENCE EQUATIONS WITH BOUNDARY CONDITIONS

Authors

Xiang Liu, Sun Yat-sen UniversityFollow
Baoguo Jia, Sun Yat-Sen UniversityFollow
Scott Gensler, University of Nebraska at KearneyFollow
Lynn Erbe, University of Nebraska-LincolnFollow
Allan Peterson, University of Nebraska - LincolnFollow

Document Type

Article

Date of this Version

2020

Citation

Electronic Journal of Differential Equations, Vol. 2020 (2020), No. 04, pp. 1–19

Comments

© 2020 Texas State University

Abstract

This article studies a boundary value problem for a nonlinear Ca- puto nabla fractional difference equation. We obtain quadratic convergence results for this equation using the generalized quasi-linearization method. Fur- ther, we obtain the convergence of the sequences is potentially improved by the Gauss-Seidel method. A numerical example illustrates our main results.