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

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.

Keywords

• caputo nabla fractional difference equation
• upper and lower solution
• generalized quasi-linearization method
• gauss-seidel method