Electron. J. Differential Equations,
Vol. 2020 (2020), No. 04, pp. 1-19.
Convergence of approximate solutions to nonlinear Caputo nabla fractional
difference equations with boundary conditions
Xiang Liu, Baoguo Jia, Scott Gensler, Lynn Erbe, Allan Peterson
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.
DOI: 10.58997/ejde.2020.04
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Xiang Liu
Sun Yat-Sen University
Guangzhou 510275, China
email: liux256@126.com
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Baoguo Jia
School of Mathematics
Sun Yat-Sen University
Guangzhou, 510275, China
email: mcsjbg@mail.sysu.edu.cn
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Scott Gensler
Department of Mathematics
University of Nebraska-Kearney
Kearney, NE 68849, USA
email: scott.gensler@gmail.com
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Lynn Erbe
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE 68588-0130, USA
email: lerbe@unl.edu
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Allan Peterson
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE 68588-0130, USA
email: apeterson1@math.unl.edu
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