Lyapunov Functions and Stability of Caputo Fractional Differential Equations with Delays
- 112 Downloads
The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.
KeywordsCaputo fractional differential equations Lyapunov functions Stability Fractional derivative of Lyapunov functions
Research was partially supported by Fund MU17-FMI-007, University of Plovdiv Paisii Hilendarski.
- 25.Sadati, S.J., Ghaderi, R., Ranjbar, A.: Some fractional comparison results and stability theorem for fractional time delay systems. Rom. Rep. Phys. 65(1), 94102 (2013)Google Scholar