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

Title: Convergence of approximate solutions to  nonlinear Caputo nabla fractional
       difference equations with boundary conditions

Authors: Xiang Liu (Sun Yat-Sen Univ., Guangzhou, China)
         Baoguo Jia (Sun Yat-Sen Univ., Guangzhou, China)
         Scott Gensler (Univ. of Nebraska, Kearney, NE, USA)
         Lynn Erbe (Univ. of Nebraska, Lincoln, NE, USA)
         Allan Peterson (Univ. of Nebraska, Lincoln, NE, USA)

Abstract:
 This article studies a boundary value problem for a
 nonlinear Caputo nabla fractional difference equation.
 We obtain quadratic convergence results for this equation
 using the generalized quasi-linearization method.
 Further, we obtain the convergence of the sequences is potentially
 improved by the Gauss-Seidel method.
 A numerical example illustrates our main results.
 
Submitted January 11, 2019. Published January 10, 2020.
Math Subject Classifications: 39A12, 39A70.
Key Words: Caputo nabla fractional difference equation; upper and lower solution;
           generalized quasi-linearization method; Gauss-Seidel method.