On the Stability of Incommensurate <i>h</i>-Nabla Fractional-Order Difference Systems

Abstract

This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with the help of using some theoretical schemes, such as the Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem and Banach fixed point theorem. These results are verified numerically via two illustrative numerical examples that show the stabilities of the solutions of systems at hand.

Keywords

• the <i>h</i>-nabla fractional-order sum operator
• incommensurate fractional-order difference systems
• <i>Z</i>-transform method
• stability analysis