A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations
This paper investigates the asymptotic eventual stability (AE-S) for nonlinear impulsive Caputo fractional differential equations (ICFDEs) with fixed impulse moments, employing auxiliary Lyapunov functions (ALF) which are specifically constructed as analogues of vector Lyapunov functions (VLF). A no...
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2024-12-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/4/4/85 |
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| author | Jackson E. Ante Michael P. Ineh Jonas O. Achuobi Uwem P. Akai Jeremiah U. Atsu Nnanake-Abasi O. Offiong |
| author_facet | Jackson E. Ante Michael P. Ineh Jonas O. Achuobi Uwem P. Akai Jeremiah U. Atsu Nnanake-Abasi O. Offiong |
| author_sort | Jackson E. Ante |
| collection | DOAJ |
| description | This paper investigates the asymptotic eventual stability (AE-S) for nonlinear impulsive Caputo fractional differential equations (ICFDEs) with fixed impulse moments, employing auxiliary Lyapunov functions (ALF) which are specifically constructed as analogues of vector Lyapunov functions (VLF). A novel derivative tailored for VLF is introduced, offering a more robust framework than existing approaches based on scalar Lyapunov functions (SLF). Adequate conditions for AE-S involving ICFDEs are provided. We also used the predictor corrector method to implement a numerical solution for a given impulsive Caputo fractional differential equation. These findings extend and improve upon existing results, providing significant advancements in the stability analysis of systems with memory effects and impulsive dynamics. The study holds practical relevance for modeling and analyzing real-world systems, including control processes, biological systems, and economic dynamics where fractional-order behavior and impulses play a crucial role. |
| format | Article |
| id | doaj-art-e220b83f36354ec797e79c1586911400 |
| institution | OA Journals |
| issn | 2673-9909 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj-art-e220b83f36354ec797e79c15869114002025-08-20T02:00:50ZengMDPI AGAppliedMath2673-99092024-12-01441600161710.3390/appliedmath4040085A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential EquationsJackson E. Ante0Michael P. Ineh1Jonas O. Achuobi2Uwem P. Akai3Jeremiah U. Atsu4Nnanake-Abasi O. Offiong5Department of Mathematics, Topfaith University, Mkpatak 530113, NigeriaDepartment of Mathematics and Computer Science, Ritman University, Ikot Ekpene 530101, NigeriaDepartment of Mathematics, University of Calabar, Calabar 540281, NigeriaDepartment of Mathematics, Topfaith University, Mkpatak 530113, NigeriaDepartment of Mathematics, University of Cross River State, Calabar 540281, NigeriaDepartment of Chemical Sciences, Topfaith University, Mkpatak 530113, NigeriaThis paper investigates the asymptotic eventual stability (AE-S) for nonlinear impulsive Caputo fractional differential equations (ICFDEs) with fixed impulse moments, employing auxiliary Lyapunov functions (ALF) which are specifically constructed as analogues of vector Lyapunov functions (VLF). A novel derivative tailored for VLF is introduced, offering a more robust framework than existing approaches based on scalar Lyapunov functions (SLF). Adequate conditions for AE-S involving ICFDEs are provided. We also used the predictor corrector method to implement a numerical solution for a given impulsive Caputo fractional differential equation. These findings extend and improve upon existing results, providing significant advancements in the stability analysis of systems with memory effects and impulsive dynamics. The study holds practical relevance for modeling and analyzing real-world systems, including control processes, biological systems, and economic dynamics where fractional-order behavior and impulses play a crucial role.https://www.mdpi.com/2673-9909/4/4/85asymptotic eventual stabilityCaputo derivativeimpulseLyapunov function |
| spellingShingle | Jackson E. Ante Michael P. Ineh Jonas O. Achuobi Uwem P. Akai Jeremiah U. Atsu Nnanake-Abasi O. Offiong A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations AppliedMath asymptotic eventual stability Caputo derivative impulse Lyapunov function |
| title | A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations |
| title_full | A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations |
| title_fullStr | A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations |
| title_full_unstemmed | A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations |
| title_short | A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations |
| title_sort | novel lyapunov asymptotic eventual stability approach for nonlinear impulsive caputo fractional differential equations |
| topic | asymptotic eventual stability Caputo derivative impulse Lyapunov function |
| url | https://www.mdpi.com/2673-9909/4/4/85 |
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