Research Article
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Year 2023, Volume: 11 Issue: 2, 241 - 251, 25.12.2023

Abdullah Yiğit

https://doi.org/10.51354/mjen.1379754

Abstract

References

  • [1]. Alkhazzan A., Wang J., Tunç C., Ding X., Yuan Z., Nie, Y., “On Existence and Continuity Results of Solution for Multi-time Scale Fractional Stochastic Differential Equation’’, Qual. Theory Dyn. Syst., 22, 49, (2023), 1-23. https://doi.org/10.1007/s12346-023-00750-x
  • [2]. Altun Y., “A new approach on the stability of fractional singular systems with time-varying delay’’, MANAS Journal of Engineering, 8(1),(2020), 59-67.
  • [3]. Altun, Y., Tunc, C., On the asymptotic stability of a nonlinear fractional-order system with multiple variable delays. Applications and Applied Mathematics: An International Journal (AAM), 15(1), (2020), 458-468.
  • [4]. Chartbupapan C., Bagdasar O., 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), 1-10.
  • [5]. Chen W., Gao F., She J., Xia W., “Further results on delay-dependent stability for neutral singular systems via state decompsition method’’, Chaos, Solitons and Fract., 141, (2020),110408.
  • [6]. Chen W., Gao F., ‘New results on stability analysis for a kind of neutral singular systems with mixed delays’’, Eur. J. Control 53, (2020), 59-67.
  • [7]. Dai L., “Singular control systems’’, Lecture Notes in Control and Information Sciences, 118. Springer-Verlag, Berlin, 1989.
  • [8]. Graef JR., Tunç C., Şevli H., “Razumikhin qualitative analyses of Volterra integro-fractional delay differential equation with Caputo derivatives’’, Commun. Nonlinear Sci. Numer. Simul.,103, (2021), 12 pp.
  • [9]. Hristova S., Tunç C., “Stability of nonlinear Volterra integro-differential equations with Caputo fractional derivative and bounded delays’’, Electron. J. Differential Equations, 30, (2019), 1-11.
  • [10]. Kilbas AA., Srivastava HM., Trujillo JJ., “Theory and Application of Fractional Differential Equations’’, Elsevier, New York, USA, 2006. [11]. Korkmaz E., Ozdemir A., “Asymptotical Stability of Riemann-Liouville Fractional Neutral Systems with Multiple Time-varying Delays’’, Applications and Applied Mathematics: An International Journal (AAM), 17, (2022) , Iss. 1, Article 7.
  • [12]. Liu S., Zhou XF., Li X., Jiang W., “Asymptotical stability of Riemann–Liouville fractional singular systems with multiple time-varying delays’’, Appl. Math. Lett., 65, (2017), 32–39.
  • [13]. Lyapunov AM., “The General Problem of the Stability of Motion’’, Üniv. Kharkov, PhD thesis, 1892.
  • [14]. Podlubny I., “Fractional Differential Equations’’, Academic Press., New York, USA, 1999.
  • [15]. Tunç C., Tunç O., “Solution estimates to Caputo proportional fractional derivative delay integro –differential equations’’, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 2023, 117, 12. [CrossRef]
  • [16]. Tunç C., “An application of Lyapunov functions to properties of solutions of a Caputo perturbed fractional differential system ’’, Int. J. Math. Comput. Sci., 17(2), (2022), 537-550.
  • [17]. Tunç O., Korkmaz E., “New Results on the Qualitative Analysis of Solutions of Vides by the Lyapunov-Razumikhin Technique ’’, Ukr Math J, 74, (2023), 1764-1779.
  • [18]. Tunç C., Yiğit A., “On the asymptotic stability of solutions of nonlinear delay differential equations’’, Journal of Mathematical Sciences, 261(2), (2022), 337–352.
  • [19].Wu Q., Song Q., Hu B., Zhao Z., Liu Y., Alsaadi FE., “Robust stability of uncertain fractional order singular systems with neutral and time-varying delays’’, Neurocomputing, 41, (2020),145-152.
  • [20].Wu ZG., Su H., Shi P., Chu J., “Analysis and synthesis of singular systems with time-delays’’, Springer-Verlag, Berlin, 2013.
  • [21]. Xu S., Lam J., “Robust control and filtering of singular systems’’, Lecture Notes in Control and Information Sciences, 332. Springer-Verlag, Berlin, 2006.
  • [22]. Yang W., Alsaedi A., Hayat T., Fardoun H.M., “Asymptotical stability analysis of Riemann-Liouville q-fractional neutral systems with mixed delays’’, Math Meth Appl Sci, 42, (2019), 4876–4888.
  • [23]. Yiğit A., Tunç C., “Asymptotical stability of nonlinear fractional neutral systems with unbounded delay’’, Applied Analysis and Optimization, 7(1), (2023), 63-77.
  • [24]. Yiğit A., Sivasundaram S., Tunç C., “Stability for fractional order delay singular systems’’, Nonlinear studies (NS), 29(3), (2022), 865-879.
  • [25]. Zhang H., Ye R., Cao J., Ahmed A., Li X., Wan Y., “Lyapunov functional approach to stability analysis of Riemann–Liouville fractional neural networks with time-varying delays. Asian J. Control, 20(5), (2018), 1938–1951.

A study on the admissibility of fractional singular systems with variable and constant delays

Year 2023, Volume: 11 Issue: 2, 241 - 251, 25.12.2023

Abdullah Yiğit

https://doi.org/10.51354/mjen.1379754

Abstract

This paper deals with fractional singular systems with mixed delays and several admissibility criteria are obtained by using Lyapunov-Krasovskii functionals, model transformation, useful lemmas, zero equations and other well-known inequalities. Finally, some numerical examples are given with graps to verify and justify the admissibility of practical systems by using our proposed methods.

Keywords

Admissibility fractional neutral singular system matrix inequality numerical illustration stability zero equation

References

  • [1]. Alkhazzan A., Wang J., Tunç C., Ding X., Yuan Z., Nie, Y., “On Existence and Continuity Results of Solution for Multi-time Scale Fractional Stochastic Differential Equation’’, Qual. Theory Dyn. Syst., 22, 49, (2023), 1-23. https://doi.org/10.1007/s12346-023-00750-x
  • [2]. Altun Y., “A new approach on the stability of fractional singular systems with time-varying delay’’, MANAS Journal of Engineering, 8(1),(2020), 59-67.
  • [3]. Altun, Y., Tunc, C., On the asymptotic stability of a nonlinear fractional-order system with multiple variable delays. Applications and Applied Mathematics: An International Journal (AAM), 15(1), (2020), 458-468.
  • [4]. Chartbupapan C., Bagdasar O., 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), 1-10.
  • [5]. Chen W., Gao F., She J., Xia W., “Further results on delay-dependent stability for neutral singular systems via state decompsition method’’, Chaos, Solitons and Fract., 141, (2020),110408.
  • [6]. Chen W., Gao F., ‘New results on stability analysis for a kind of neutral singular systems with mixed delays’’, Eur. J. Control 53, (2020), 59-67.
  • [7]. Dai L., “Singular control systems’’, Lecture Notes in Control and Information Sciences, 118. Springer-Verlag, Berlin, 1989.
  • [8]. Graef JR., Tunç C., Şevli H., “Razumikhin qualitative analyses of Volterra integro-fractional delay differential equation with Caputo derivatives’’, Commun. Nonlinear Sci. Numer. Simul.,103, (2021), 12 pp.
  • [9]. Hristova S., Tunç C., “Stability of nonlinear Volterra integro-differential equations with Caputo fractional derivative and bounded delays’’, Electron. J. Differential Equations, 30, (2019), 1-11.
  • [10]. Kilbas AA., Srivastava HM., Trujillo JJ., “Theory and Application of Fractional Differential Equations’’, Elsevier, New York, USA, 2006. [11]. Korkmaz E., Ozdemir A., “Asymptotical Stability of Riemann-Liouville Fractional Neutral Systems with Multiple Time-varying Delays’’, Applications and Applied Mathematics: An International Journal (AAM), 17, (2022) , Iss. 1, Article 7.
  • [12]. Liu S., Zhou XF., Li X., Jiang W., “Asymptotical stability of Riemann–Liouville fractional singular systems with multiple time-varying delays’’, Appl. Math. Lett., 65, (2017), 32–39.
  • [13]. Lyapunov AM., “The General Problem of the Stability of Motion’’, Üniv. Kharkov, PhD thesis, 1892.
  • [14]. Podlubny I., “Fractional Differential Equations’’, Academic Press., New York, USA, 1999.
  • [15]. Tunç C., Tunç O., “Solution estimates to Caputo proportional fractional derivative delay integro –differential equations’’, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 2023, 117, 12. [CrossRef]
  • [16]. Tunç C., “An application of Lyapunov functions to properties of solutions of a Caputo perturbed fractional differential system ’’, Int. J. Math. Comput. Sci., 17(2), (2022), 537-550.
  • [17]. Tunç O., Korkmaz E., “New Results on the Qualitative Analysis of Solutions of Vides by the Lyapunov-Razumikhin Technique ’’, Ukr Math J, 74, (2023), 1764-1779.
  • [18]. Tunç C., Yiğit A., “On the asymptotic stability of solutions of nonlinear delay differential equations’’, Journal of Mathematical Sciences, 261(2), (2022), 337–352.
  • [19].Wu Q., Song Q., Hu B., Zhao Z., Liu Y., Alsaadi FE., “Robust stability of uncertain fractional order singular systems with neutral and time-varying delays’’, Neurocomputing, 41, (2020),145-152.
  • [20].Wu ZG., Su H., Shi P., Chu J., “Analysis and synthesis of singular systems with time-delays’’, Springer-Verlag, Berlin, 2013.
  • [21]. Xu S., Lam J., “Robust control and filtering of singular systems’’, Lecture Notes in Control and Information Sciences, 332. Springer-Verlag, Berlin, 2006.
  • [22]. Yang W., Alsaedi A., Hayat T., Fardoun H.M., “Asymptotical stability analysis of Riemann-Liouville q-fractional neutral systems with mixed delays’’, Math Meth Appl Sci, 42, (2019), 4876–4888.
  • [23]. Yiğit A., Tunç C., “Asymptotical stability of nonlinear fractional neutral systems with unbounded delay’’, Applied Analysis and Optimization, 7(1), (2023), 63-77.
  • [24]. Yiğit A., Sivasundaram S., Tunç C., “Stability for fractional order delay singular systems’’, Nonlinear studies (NS), 29(3), (2022), 865-879.
  • [25]. Zhang H., Ye R., Cao J., Ahmed A., Li X., Wan Y., “Lyapunov functional approach to stability analysis of Riemann–Liouville fractional neural networks with time-varying delays. Asian J. Control, 20(5), (2018), 1938–1951.
There are 24 citations in total.

Details

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

Abdullah Yiğit 0000-0002-0099-3095

Publication Date December 25, 2023
Submission Date October 22, 2023
Acceptance Date December 6, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

APA Yiğit, A. (2023). A study on the admissibility of fractional singular systems with variable and constant delays. MANAS Journal of Engineering, 11(2), 241-251. https://doi.org/10.51354/mjen.1379754
AMA Yiğit A. A study on the admissibility of fractional singular systems with variable and constant delays. MJEN. December 2023;11(2):241-251. doi:10.51354/mjen.1379754
Chicago Yiğit, Abdullah. “A Study on the Admissibility of Fractional Singular Systems With Variable and Constant Delays”. MANAS Journal of Engineering 11, no. 2 (December 2023): 241-51. https://doi.org/10.51354/mjen.1379754.
EndNote Yiğit A (December 1, 2023) A study on the admissibility of fractional singular systems with variable and constant delays. MANAS Journal of Engineering 11 2 241–251.
IEEE A. Yiğit, “A study on the admissibility of fractional singular systems with variable and constant delays”, MJEN, vol. 11, no. 2, pp. 241–251, 2023, doi: 10.51354/mjen.1379754.
ISNAD Yiğit, Abdullah. “A Study on the Admissibility of Fractional Singular Systems With Variable and Constant Delays”. MANAS Journal of Engineering 11/2 (December 2023), 241-251. https://doi.org/10.51354/mjen.1379754.
JAMA Yiğit A. A study on the admissibility of fractional singular systems with variable and constant delays. MJEN. 2023;11:241–251.
MLA Yiğit, Abdullah. “A Study on the Admissibility of Fractional Singular Systems With Variable and Constant Delays”. MANAS Journal of Engineering, vol. 11, no. 2, 2023, pp. 241-5, doi:10.51354/mjen.1379754.
Vancouver Yiğit A. A study on the admissibility of fractional singular systems with variable and constant delays. MJEN. 2023;11(2):241-5.
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