On the Novel Auxiliary Lyapunov Function and Uniform Asymptotic Practical Stability of Nonlinear Impulsive Caputo Fractional Differential Equations via New Modelled Generalized Dini Derivative.

Jackson Ante; Okoi Itam; Jeremiah Atsu; Samuel Essang; Etimbuk Abraham; Michael Ineh

doi:10.52589/AJMSS-VUNAIOBC

On the Novel Auxiliary Lyapunov Function and Uniform Asymptotic Practical Stability of Nonlinear Impulsive Caputo Fractional Differential Equations via New Modelled Generalized Dini Derivative. | AB Journals

On the Novel Auxiliary Lyapunov Function and Uniform Asymptotic Practical Stability of Nonlinear Impulsive Caputo Fractional Differential Equations via New Modelled Generalized Dini Derivative.

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African Journal of Mathematics and Statistics Studies

Vol. 7Issue 42024pp. 11–33Published 26 September 2024

DOI 10.52589/AJMSS-VUNAIOBC

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Abstract:

In this paper, the uniform asymptotic practical stability of nonlinear impulsive Caputo fractional differential equations with fixed moment of impulse is examined using an auxilliary Lyapunov functions which are analogues of vector Lyapunov functions. Together with comparison results, sufficient conditions for the uniform practical stability as well as the uniform asymptotic practical stability of the impulsive Caputo fractional order systems are established. An illustrative example is given to confirm the suitability of the obtained results.

Keywords:Uniform asymptotic practical stability Caputo derivative impulse Lyapunov function.

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