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On the controllability of nonlinear fractional system with control delay

Yıl 2020, Cilt: 49 Sayı: 1, 294 - 302, 06.02.2020
https://doi.org/10.15672/hujms.546990

Öz

We discuss the controllability of nonlinear fractional control system with control delay. Firstly we obtain result about controllability of a linear fractional control system. After that, we give sufficient condition for the controllability of nonlinear fractional system with control delay. Our approach is based on Schauder fixed point theorem. At the end numerical example is constructed to support the result.

Kaynakça

  • [1] J.O. Alzabut, Existence of periodic solutions of a type of nonlinear impulsive delay differential equations with a small parameter, J. Nonlinear Math. Phys. 15, 13–21, 2008.
  • [2] K. Balachandran, J.P. Dauer, Controllability of nonlinear systems via fixed-point theorems, J. Optim. Theory Appl. 53 (3), 345–352, 1987.
  • [3] K. Balachandran, V. Govindaraj, L. Rodriguez-Germa, and J.J. Trujillo, Controllability of nonlinear higher order fractional dynamical systems, Nonlinear Dynam. 156, 33–44, 2013.
  • [4] K. Balachandran, J.Y. Park, and J.J. Trujillo, Controllability of nonlinear fractional dynamical systems, Nonlinear Anal. 75 (4), 1919–1926, 2012.
  • [5] L. Dai, Singular Control Systems, Springer, 1989.
  • [6] J.P. Dauer, Nonlinear Perturbations of Quasi-Linear Control Systems, J. Math. Anal. Appl. 54, 717–725, 1976.
  • [7] J.P. Dauer, R.D. Gahl, Controllability of nonlinear delay systems, J. Optimiz. Theory Appl. 21 (1), 59–70, 1977.
  • [8] Park, K. Diethel, The analysis of fractional differential equations, Lect. Notes Math., 2010.
  • [9] J. Hale, Introduction to functional differential equations, Springer Verlag, 1992.
  • [10] W. Jiang, The degeneration differential systems with delay, Anhui University Press, 1998.
  • [11] W. Jiang, Eigenvalue and stability of singular differential delay systems, J. Math. Anal. Appl. 297, 305–316, 2004.
  • [12] W. Jiang, Function-controllability of nonlinear singular delay differential control systems, Acta Math. Sinica (Chin. Ser.) 49 (5), 1153–1162, 2006.
  • [13] W. Jiang, On the solvability of singular differential delay systems with variable coefficients, Int. J. Dyn. Syst. Differ. Equ. 4, 245–249, 2008.
  • [14] W. Jiang, The constant variation formulae for singular fractional differential systems with delay, Comput. Math. Appl. 59 (3), 1184–1190, 2010.
  • [15] W. Jiang, The controllability of fractional control systems with control delay, Comput. Math. Appl. 64, 3153–3159, 2012.
  • [16] W. Jiang, On the interval controllability of fractional systems with control delay, J. Math. Res. 9 (5), 87, 2017.
  • [17] W. Jiang and W. Song, Controllability of singular systems with control delay, Automatica J. IFAC 37, 1873–1877, 2001.
  • [18] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science Publishers, 204, 2006.
  • [19] K.S. Miller and B. Ross, An introduction to the fractional calculus and differential equations, John Wiley and Sons, 1993.
  • [20] R.J. Nirmala, K. Balachandran, L.R. Germa, and J.J. Trujillo, Controllability of nonlinear fractional delay dynamical systems, Rep. Math. Phys. 77 (1), 87–104, 2016.
  • [21] I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
Yıl 2020, Cilt: 49 Sayı: 1, 294 - 302, 06.02.2020
https://doi.org/10.15672/hujms.546990

Öz

Kaynakça

  • [1] J.O. Alzabut, Existence of periodic solutions of a type of nonlinear impulsive delay differential equations with a small parameter, J. Nonlinear Math. Phys. 15, 13–21, 2008.
  • [2] K. Balachandran, J.P. Dauer, Controllability of nonlinear systems via fixed-point theorems, J. Optim. Theory Appl. 53 (3), 345–352, 1987.
  • [3] K. Balachandran, V. Govindaraj, L. Rodriguez-Germa, and J.J. Trujillo, Controllability of nonlinear higher order fractional dynamical systems, Nonlinear Dynam. 156, 33–44, 2013.
  • [4] K. Balachandran, J.Y. Park, and J.J. Trujillo, Controllability of nonlinear fractional dynamical systems, Nonlinear Anal. 75 (4), 1919–1926, 2012.
  • [5] L. Dai, Singular Control Systems, Springer, 1989.
  • [6] J.P. Dauer, Nonlinear Perturbations of Quasi-Linear Control Systems, J. Math. Anal. Appl. 54, 717–725, 1976.
  • [7] J.P. Dauer, R.D. Gahl, Controllability of nonlinear delay systems, J. Optimiz. Theory Appl. 21 (1), 59–70, 1977.
  • [8] Park, K. Diethel, The analysis of fractional differential equations, Lect. Notes Math., 2010.
  • [9] J. Hale, Introduction to functional differential equations, Springer Verlag, 1992.
  • [10] W. Jiang, The degeneration differential systems with delay, Anhui University Press, 1998.
  • [11] W. Jiang, Eigenvalue and stability of singular differential delay systems, J. Math. Anal. Appl. 297, 305–316, 2004.
  • [12] W. Jiang, Function-controllability of nonlinear singular delay differential control systems, Acta Math. Sinica (Chin. Ser.) 49 (5), 1153–1162, 2006.
  • [13] W. Jiang, On the solvability of singular differential delay systems with variable coefficients, Int. J. Dyn. Syst. Differ. Equ. 4, 245–249, 2008.
  • [14] W. Jiang, The constant variation formulae for singular fractional differential systems with delay, Comput. Math. Appl. 59 (3), 1184–1190, 2010.
  • [15] W. Jiang, The controllability of fractional control systems with control delay, Comput. Math. Appl. 64, 3153–3159, 2012.
  • [16] W. Jiang, On the interval controllability of fractional systems with control delay, J. Math. Res. 9 (5), 87, 2017.
  • [17] W. Jiang and W. Song, Controllability of singular systems with control delay, Automatica J. IFAC 37, 1873–1877, 2001.
  • [18] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science Publishers, 204, 2006.
  • [19] K.S. Miller and B. Ross, An introduction to the fractional calculus and differential equations, John Wiley and Sons, 1993.
  • [20] R.J. Nirmala, K. Balachandran, L.R. Germa, and J.J. Trujillo, Controllability of nonlinear fractional delay dynamical systems, Rep. Math. Phys. 77 (1), 87–104, 2016.
  • [21] I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Musarrat Nawaz 0000-0001-6418-1283

Jiang Wei Bu kişi benim 0000-0002-5446-1860

Jiale Sheng Bu kişi benim 0000-0003-0207-9712

Azmat Ullah Khan Niazi Bu kişi benim 0000-0001-9114-8075

Lichang Yang Bu kişi benim 0000-0002-5555-3433

Yayımlanma Tarihi 6 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 1

Kaynak Göster

APA Nawaz, M., Wei, J., Sheng, J., Ullah Khan Niazi, A., vd. (2020). On the controllability of nonlinear fractional system with control delay. Hacettepe Journal of Mathematics and Statistics, 49(1), 294-302. https://doi.org/10.15672/hujms.546990
AMA Nawaz M, Wei J, Sheng J, Ullah Khan Niazi A, Yang L. On the controllability of nonlinear fractional system with control delay. Hacettepe Journal of Mathematics and Statistics. Şubat 2020;49(1):294-302. doi:10.15672/hujms.546990
Chicago Nawaz, Musarrat, Jiang Wei, Jiale Sheng, Azmat Ullah Khan Niazi, ve Lichang Yang. “On the Controllability of Nonlinear Fractional System With Control Delay”. Hacettepe Journal of Mathematics and Statistics 49, sy. 1 (Şubat 2020): 294-302. https://doi.org/10.15672/hujms.546990.
EndNote Nawaz M, Wei J, Sheng J, Ullah Khan Niazi A, Yang L (01 Şubat 2020) On the controllability of nonlinear fractional system with control delay. Hacettepe Journal of Mathematics and Statistics 49 1 294–302.
IEEE M. Nawaz, J. Wei, J. Sheng, A. Ullah Khan Niazi, ve L. Yang, “On the controllability of nonlinear fractional system with control delay”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, ss. 294–302, 2020, doi: 10.15672/hujms.546990.
ISNAD Nawaz, Musarrat vd. “On the Controllability of Nonlinear Fractional System With Control Delay”. Hacettepe Journal of Mathematics and Statistics 49/1 (Şubat 2020), 294-302. https://doi.org/10.15672/hujms.546990.
JAMA Nawaz M, Wei J, Sheng J, Ullah Khan Niazi A, Yang L. On the controllability of nonlinear fractional system with control delay. Hacettepe Journal of Mathematics and Statistics. 2020;49:294–302.
MLA Nawaz, Musarrat vd. “On the Controllability of Nonlinear Fractional System With Control Delay”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, 2020, ss. 294-02, doi:10.15672/hujms.546990.
Vancouver Nawaz M, Wei J, Sheng J, Ullah Khan Niazi A, Yang L. On the controllability of nonlinear fractional system with control delay. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):294-302.