Existence and rapid convergence results for nonlinear Caputo nabla fractional difference equations

Abstract

This paper is concerned with finding properties of solutions to initial value problems for nonlinear Caputo nabla fractional difference equations. We obtain existence and rapid convergence results for such equations by use of Schauder's fixed point theorem and the generalized quasi-linearization method, respectively. A numerical example is given to illustrate one of our rapid convergence results.

Keywords

• caputo nabla fractional difference equation
• schauder's fixed point theorem
• generalized quasi-linearization
• existence
• rapid convergence