LYAPUNOV UNIFORM ASYMPTOTIC STABILITY OF CAPUTO FRACTIONAL DYNAMIC EQUATIONS ON TIME SCALE USING A GENERALIZED DERIVATIVE

In this work, we establish the uniform asymptotic stability using a generalized concept (herein referred to as Caputo fractional delta derivative and Caputo fractional delta Dini derivative of order α ∈ (0,1) for Caputo fractional derivatives on an arbitrary time domain T, which is a closed subset of R. Combining the continuous and discrete time domains, we create a unified framework for uniform asymptotic stability analysis on time scales. This work also incorporates an illustrative example to demonstrate the relevance, effectiveness, and applicability of the established stability results over that of the integer order.