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

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 Ga...

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Bibliographic Details
Published in:Electronic journal of differential equations 2020-01, Vol.2020 (4), p.1-19
Main Authors: Xiang Liu, Baoguo Jia, Scott Gensler, Lynn Erbe, Allan Peterson
Format: Article
Language:English
Subjects:
caputo nabla fractional difference equation
gauss-seidel method
generalized quasi-linearization method
upper and lower solution
Online Access:Get full text
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Summary: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.
ISSN:1072-6691