Stability of nonlinear q-fractional dynamical systems on time scale

Abstract

This paper adopts a new terminology, “delta q-Mittag-Leffler stability”, for studying the stability of nonlinear q-fractional dynamical systems on the time scale. In fact, the idea of delta q-Mittag-Leffler stability is inspired by the idea of Mittag-Leffler stability, which is designed to investigate the stability of fractional dynamical systems. The sufficient conditions for delta q-Mittag-Leffler stability of considered dynamical systems with Caputo delta q-derivatives have been introduced.

Keywords

• q-fractional calculus
• q-Mittag-Leffler function
• Time scale calculus
• q-Mittag-Leffler stability