On the Existence of Maximal Solution and Lyapunov Practical Stability of Nonlinear Impulsive Caputo Fractional Derivative via Comparison Principle.

Jackson Efiong Ante; Samuel Okon Essang; Okoi Okoi Itam; Etorti Imoke John

doi:10.52589/AJSTE-9BWUJX9O

On the Existence of Maximal Solution and Lyapunov Practical Stability of Nonlinear Impulsive Caputo Fractional Derivative via Comparison Principle.

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Advanced Journal of Science, Technology and Engineering

Vol. 4Issue 42024pp. 92–110Published 30 October 2024

DOI 10.52589/AJSTE-9BWUJX9O

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Abstract:

This paper examines the existence of maximal solution of the comparison differential system and also establishes sufficient conditions for the practical stability of the trivial solution of a nonlinear impulsive Caputo fractional differential system with fixed moment of impulse using the vector Lyapunov functions. First, it was discovered that the vector form of the Lyapunov function was majorized by the maximal solution of the comparison system. From the results obtained, it was established that the main system is practically stable in the sense of Lyapunov.

Keywords:practical stability Caputo derivative impulse vector Lyapunov functions fractional differential equations maximal solution.

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