Existence and stability of solutions of totally nonlinear neutral caputo nabla fractional difference equations

Abstract

This thesis examines the existence and stability of solutions for a class of to- tally nonlinear neutral nabla fractional difference equations of the Caputo type of order α € (0,1). Fixed point theory is used extensively in this thesis to investi- gate the existence and stability of solutions of these equations. In particular, the Krasnoselskii-Burton fixed point theorem is used in the thesis. In the analysis, the totally nonlinear neutral Caputo nabla fractional difference equations are trans- formed into equivalent summation equations. The resulting summation equations are then decomposed into appropriate mappings, specifically a large contraction and a compact mapping. By employing the Krasnoselskii-Burton’s fixed-point theorem, sufficient conditions for the existence of solutions to these equations are obtained. Furthermore, sufficient criteria for the stability of solutions to these equations are also obtained. In addition, two examples are provided to demon- strate the applicability of the main theorems. The results obtained in this study extend and generalise previous findings in the literature.