Research Article
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Year 2025, Volume: 13 Issue: 1, 30 - 39, 27.06.2025

Yener Altun

https://doi.org/10.51354/mjen.1575022

Abstract

References

  • [1]. Agarwal, R.P., “Certain fractional q-integrals and q-derivatives,” Proc Cambridge Philos Soc., 66, (1969), pp. 365-370.
  • [2]. Agarwal, R.P., Benchohra, M., Hamani, S., “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions,” Acta Appl. Math., 109 (3), (2010), pp. 973-1033.
  • [3]. Al-Salam, WA., “Some fractional q-integrals and q-derivatives,” Proc Edin Math Soc., 15, (1969), pp. 135-140.
  • [4]. Altun, Y. and Tunç, C., “On exponential stability of solutions of nonlinear neutral differential systems with discrete and distributed variable lags,” Nonlinear Studies 26(2), (2019), pp. 455-466.
  • [5]. Annaby, M.H. and Mansour, Z.S., “Q-fractional Calculus and Equations,” New York: Springer-Heidelberg; 2012.
  • [6]. Balasubramaniam, P., Krishnasamy, R. and Rakkiyappan, R., “Delay- dependent stability of neutral systems with time-varying delays using delay-decomposition approach,” Applied Mathematical Modelling 36, (2012), pp. 2253–2261.
  • [7]. Bohner, M. and Peterson, A., “Dynamic Equations on Time Scales: An Introduction with Applications,” Boston: Birkhäuser, 2001.
  • [8]. Chartbupapan, C., Bagdasar, O. and Mukdasai, K., “A Novel Delay- Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation,” Mathematics, 8, (2020), pp. 1-10.
  • [9]. Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A. and Castro-Linares, R., “Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems,” Commun. Nonlinear Sci. Numer. Simul., 22, (2015), pp. 650–659.
  • [10]. Diethelm, K., “The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type,” Berlin: Springer, 2010.
  • [11]. Jarad, F., Abdeljawad, T. and Baleanu D., “Stability of q-fractional non-autonomous systems,” Nonlinear Anal RealWorld Appl., 14, (2013b), pp. 780-784.
  • [12]. Kac, V. and Cheung, P., “Quantum calculus,” New York: Springer- Verlag, 2002.
  • [13]. Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., “Theory and Application of Fractional Differential Equations,” Elsevier, New York: USA, 2006.
  • [14]. Koca, I. and Demirci, E., “On local asymptotic stability of q-fractional nonlinear dynamical systems,” Applications and Applied Mathematics: An International Journal (AAM), 11, (2016), pp. 174-183.
  • [15]. Li, H. Zhou, S. and Li, H., “Asymptotic stability analysis of fractional- order neutral systems with time delay,” Adv. Difference Equ., 2015, (2015), pp. 325–335.
  • [16]. Liu, K. and Jiang, W., “Stability of fractional neutral systems,” Adv. Differ. Equ., 2014(78), (2014), pp. 1-9
  • [17]. Liu P.L., “A delay decomposition approach to stability analysis of neutral systems with time‐varying delay,” App Math Model., 37, (2013), pp. 5013‐5026.
  • [18]. Liu, S., Jiang, W., Li, X. and Zhou, X.F., “Lyapunov stability analysis of fractional nonlinear systems,” Appl. Math. Lett., 51, (2016), pp. 13–19.
  • [19]. Liu, S., Wu, X. Zhang, Y.J. and Yang, R., “Asymptotical stability of Riemann–Liouville fractional neutral systems,” Appl. Math. Lett., 69, (2017), pp. 168–173.
  • [20]. Liu, S., Wu, X., Zhou, X.F. and Jiang, W., “Asymptotical stability of Riemann–Liouville fractional nonlinear systems,” Nonlinear Dynam., 86(1), (2016), pp. 65–71.
  • [21]. Liu, S., Zhou, X.F., Li, X. and Jiang, W., “Stability of fractional nonlinear singular systems its applications in synchronization of complex dynamical networks,” Nonlinear Dynam., 84(4), (2016), pp. 2377–2385.
  • [22]. Liu, S., Zhou, X.F., Li, X. and Jiang, W., “Asymptotical stability of Riemann–Liouville fractional singular systems with multiple time- varying delays,” Appl. Math. Lett., 65, (2017), pp. 32–39.
  • [23]. Lu, J.G. and Chen, G., “Robust stability and stabilization of fractional-order interval systems: An LMI approach,” IEEE Trans. Automat. Control, 54 (6), (2009), pp. 1294–1299.
  • [24]. Lu, Y.F., Wu, R.C. and Qin, Z.Q., “Asymptotic stability of nonlinear fractional neutral singular systems,” J. Appl. Math. Comput., 45, (2014), pp. 351–364.
  • [25]. Magin, R., “Fractional calculus models of complex dynamics in biological tissues,” Comput. Math. Appl., 59, (2010), pp. 1586-1593.
  • [26]. Mahdi, N.K. and Khudair, A.R., “Stability of nonlinear q-fractional dynamical systems on time scale,” Partial Differ. Equ. Appl. Math., 7, (2023), 100496.
  • [27]. Metzler, R. and Klafter, J., “The random walk’s guide to anomalous diffusion: a fractional Dynamics approach,” Phys. Rep., 339, (2000), pp. 1-77.
  • [28]. Podlubny, I., Fractional Differential Equations, Academic Press., New York: USA, 1999.
  • [29]. Rostek, S. and Schobel, R., “A note on the use of fractional Brownian motion for financial modeling,” Econ Model., 30, (2013), pp. 30- 35.
  • [30]. Sabatier, J., Moze, M. and Farges, C., “LMI stability conditions for fractional order systems,” Comput. Math. Appl., 59 (5), (2010), pp. 1594- 1609.
  • [31]. Singh, A., Shukla, A., Vijayakumar, V. and Udhayakumar, R., "Asymptotic stability of fractional order (1, 2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, 150, (2021), pp. 1-9.
  • [32]. Sivasankar, S. and Udhayakumar, R., “Hilfer fractional neutral stochastic Volterra integro-differential inclusions via almost sectorial operators,” Mathematics, 10(12), (2022), pp. 1-19.
  • [33]. Xu, S. and Lam, J., “Robust control and filtering of singular systems,” Lecture Notes in Control and Information Sciences, 29 332, Springer- Verlag, Berlin, 2006.
  • [34]. Varun Bose, C. B. S. and Udhayakumar, R., “Existence of mild solutions for Hilfer fractional neutral integro differential inclusions via almost sectorial operators,” Fractal and Fractional, 6(9), (2022), pp. 1-16.
  • [35]. Yang, W., Alsaedi, A., Hayat, T. and Fardoun, H.M., “Asymptotical stability analysis of Riemann-Liouville q-fractional neutral systems with mixed delays,” Math. Meth. Appl. Sci., 42, (2019), pp. 4876–4888.
  • [36]. Yang, C., Zhang, Q. and Zhou, L., “Stability analysis and design for nonlinear singular systems,” Lecture Notes in Control 31 and Information Sciences, 435, Springer, Heidelberg, 2013.
  • [37]. Zhang, H., Ye, R., Cao, J., Ahmed, A., Li, X. and Ying, W., “Lyapunov functional approach to stability analysis of Riemann–Liouville fractional neural networks with time-varying delays,” Asian J. Control, 20(5), (2018), pp. 1938–1951.

An investigation into the asymptotic stability analysis of delayed q-fractional neutral systems

Year 2025, Volume: 13 Issue: 1, 30 - 39, 27.06.2025

Yener Altun

https://doi.org/10.51354/mjen.1575022

Abstract

This research analyzes the asymptotic stability of delayed q-fractional neutral systems. By developing suitable Lyapunov-Krasovskii functionals (LKFs), certain sufficient conditions for asymptotic stability are derived using linear matrix inequalities (LMIs). The approach used in this paper relies on directly calculating the quantum derivatives of the LKFs. Lastly, we provide two numerical examples to demonstrate how our theoretical findings can be applied.

Keywords

asymptotic stability q-fractional neutral systems LKF LMI

References

  • [1]. Agarwal, R.P., “Certain fractional q-integrals and q-derivatives,” Proc Cambridge Philos Soc., 66, (1969), pp. 365-370.
  • [2]. Agarwal, R.P., Benchohra, M., Hamani, S., “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions,” Acta Appl. Math., 109 (3), (2010), pp. 973-1033.
  • [3]. Al-Salam, WA., “Some fractional q-integrals and q-derivatives,” Proc Edin Math Soc., 15, (1969), pp. 135-140.
  • [4]. Altun, Y. and Tunç, C., “On exponential stability of solutions of nonlinear neutral differential systems with discrete and distributed variable lags,” Nonlinear Studies 26(2), (2019), pp. 455-466.
  • [5]. Annaby, M.H. and Mansour, Z.S., “Q-fractional Calculus and Equations,” New York: Springer-Heidelberg; 2012.
  • [6]. Balasubramaniam, P., Krishnasamy, R. and Rakkiyappan, R., “Delay- dependent stability of neutral systems with time-varying delays using delay-decomposition approach,” Applied Mathematical Modelling 36, (2012), pp. 2253–2261.
  • [7]. Bohner, M. and Peterson, A., “Dynamic Equations on Time Scales: An Introduction with Applications,” Boston: Birkhäuser, 2001.
  • [8]. Chartbupapan, C., Bagdasar, O. and Mukdasai, K., “A Novel Delay- Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation,” Mathematics, 8, (2020), pp. 1-10.
  • [9]. Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A. and Castro-Linares, R., “Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems,” Commun. Nonlinear Sci. Numer. Simul., 22, (2015), pp. 650–659.
  • [10]. Diethelm, K., “The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type,” Berlin: Springer, 2010.
  • [11]. Jarad, F., Abdeljawad, T. and Baleanu D., “Stability of q-fractional non-autonomous systems,” Nonlinear Anal RealWorld Appl., 14, (2013b), pp. 780-784.
  • [12]. Kac, V. and Cheung, P., “Quantum calculus,” New York: Springer- Verlag, 2002.
  • [13]. Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., “Theory and Application of Fractional Differential Equations,” Elsevier, New York: USA, 2006.
  • [14]. Koca, I. and Demirci, E., “On local asymptotic stability of q-fractional nonlinear dynamical systems,” Applications and Applied Mathematics: An International Journal (AAM), 11, (2016), pp. 174-183.
  • [15]. Li, H. Zhou, S. and Li, H., “Asymptotic stability analysis of fractional- order neutral systems with time delay,” Adv. Difference Equ., 2015, (2015), pp. 325–335.
  • [16]. Liu, K. and Jiang, W., “Stability of fractional neutral systems,” Adv. Differ. Equ., 2014(78), (2014), pp. 1-9
  • [17]. Liu P.L., “A delay decomposition approach to stability analysis of neutral systems with time‐varying delay,” App Math Model., 37, (2013), pp. 5013‐5026.
  • [18]. Liu, S., Jiang, W., Li, X. and Zhou, X.F., “Lyapunov stability analysis of fractional nonlinear systems,” Appl. Math. Lett., 51, (2016), pp. 13–19.
  • [19]. Liu, S., Wu, X. Zhang, Y.J. and Yang, R., “Asymptotical stability of Riemann–Liouville fractional neutral systems,” Appl. Math. Lett., 69, (2017), pp. 168–173.
  • [20]. Liu, S., Wu, X., Zhou, X.F. and Jiang, W., “Asymptotical stability of Riemann–Liouville fractional nonlinear systems,” Nonlinear Dynam., 86(1), (2016), pp. 65–71.
  • [21]. Liu, S., Zhou, X.F., Li, X. and Jiang, W., “Stability of fractional nonlinear singular systems its applications in synchronization of complex dynamical networks,” Nonlinear Dynam., 84(4), (2016), pp. 2377–2385.
  • [22]. Liu, S., Zhou, X.F., Li, X. and Jiang, W., “Asymptotical stability of Riemann–Liouville fractional singular systems with multiple time- varying delays,” Appl. Math. Lett., 65, (2017), pp. 32–39.
  • [23]. Lu, J.G. and Chen, G., “Robust stability and stabilization of fractional-order interval systems: An LMI approach,” IEEE Trans. Automat. Control, 54 (6), (2009), pp. 1294–1299.
  • [24]. Lu, Y.F., Wu, R.C. and Qin, Z.Q., “Asymptotic stability of nonlinear fractional neutral singular systems,” J. Appl. Math. Comput., 45, (2014), pp. 351–364.
  • [25]. Magin, R., “Fractional calculus models of complex dynamics in biological tissues,” Comput. Math. Appl., 59, (2010), pp. 1586-1593.
  • [26]. Mahdi, N.K. and Khudair, A.R., “Stability of nonlinear q-fractional dynamical systems on time scale,” Partial Differ. Equ. Appl. Math., 7, (2023), 100496.
  • [27]. Metzler, R. and Klafter, J., “The random walk’s guide to anomalous diffusion: a fractional Dynamics approach,” Phys. Rep., 339, (2000), pp. 1-77.
  • [28]. Podlubny, I., Fractional Differential Equations, Academic Press., New York: USA, 1999.
  • [29]. Rostek, S. and Schobel, R., “A note on the use of fractional Brownian motion for financial modeling,” Econ Model., 30, (2013), pp. 30- 35.
  • [30]. Sabatier, J., Moze, M. and Farges, C., “LMI stability conditions for fractional order systems,” Comput. Math. Appl., 59 (5), (2010), pp. 1594- 1609.
  • [31]. Singh, A., Shukla, A., Vijayakumar, V. and Udhayakumar, R., "Asymptotic stability of fractional order (1, 2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, 150, (2021), pp. 1-9.
  • [32]. Sivasankar, S. and Udhayakumar, R., “Hilfer fractional neutral stochastic Volterra integro-differential inclusions via almost sectorial operators,” Mathematics, 10(12), (2022), pp. 1-19.
  • [33]. Xu, S. and Lam, J., “Robust control and filtering of singular systems,” Lecture Notes in Control and Information Sciences, 29 332, Springer- Verlag, Berlin, 2006.
  • [34]. Varun Bose, C. B. S. and Udhayakumar, R., “Existence of mild solutions for Hilfer fractional neutral integro differential inclusions via almost sectorial operators,” Fractal and Fractional, 6(9), (2022), pp. 1-16.
  • [35]. Yang, W., Alsaedi, A., Hayat, T. and Fardoun, H.M., “Asymptotical stability analysis of Riemann-Liouville q-fractional neutral systems with mixed delays,” Math. Meth. Appl. Sci., 42, (2019), pp. 4876–4888.
  • [36]. Yang, C., Zhang, Q. and Zhou, L., “Stability analysis and design for nonlinear singular systems,” Lecture Notes in Control 31 and Information Sciences, 435, Springer, Heidelberg, 2013.
  • [37]. Zhang, H., Ye, R., Cao, J., Ahmed, A., Li, X. and Ying, W., “Lyapunov functional approach to stability analysis of Riemann–Liouville fractional neural networks with time-varying delays,” Asian J. Control, 20(5), (2018), pp. 1938–1951.
There are 37 citations in total.

Details

Primary Language English
Subjects Dynamical Systems in Applications
Journal Section Research Article
Authors

Yener Altun 0000-0003-1073-5513

Publication Date June 27, 2025
Submission Date October 28, 2024
Acceptance Date March 12, 2025
Published in Issue Year 2025 Volume: 13 Issue: 1

Cite

APA Altun, Y. (2025). An investigation into the asymptotic stability analysis of delayed q-fractional neutral systems. MANAS Journal of Engineering, 13(1), 30-39. https://doi.org/10.51354/mjen.1575022
AMA Altun Y. An investigation into the asymptotic stability analysis of delayed q-fractional neutral systems. MJEN. June 2025;13(1):30-39. doi:10.51354/mjen.1575022
Chicago Altun, Yener. “An Investigation into the Asymptotic Stability Analysis of Delayed Q-Fractional Neutral Systems”. MANAS Journal of Engineering 13, no. 1 (June 2025): 30-39. https://doi.org/10.51354/mjen.1575022.
EndNote Altun Y (June 1, 2025) An investigation into the asymptotic stability analysis of delayed q-fractional neutral systems. MANAS Journal of Engineering 13 1 30–39.
IEEE Y. Altun, “An investigation into the asymptotic stability analysis of delayed q-fractional neutral systems”, MJEN, vol. 13, no. 1, pp. 30–39, 2025, doi: 10.51354/mjen.1575022.
ISNAD Altun, Yener. “An Investigation into the Asymptotic Stability Analysis of Delayed Q-Fractional Neutral Systems”. MANAS Journal of Engineering 13/1 (June 2025), 30-39. https://doi.org/10.51354/mjen.1575022.
JAMA Altun Y. An investigation into the asymptotic stability analysis of delayed q-fractional neutral systems. MJEN. 2025;13:30–39.
MLA Altun, Yener. “An Investigation into the Asymptotic Stability Analysis of Delayed Q-Fractional Neutral Systems”. MANAS Journal of Engineering, vol. 13, no. 1, 2025, pp. 30-39, doi:10.51354/mjen.1575022.
Vancouver Altun Y. An investigation into the asymptotic stability analysis of delayed q-fractional neutral systems. MJEN. 2025;13(1):30-9.
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