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Asymptotic stability in Caputo-Hadamard fractional dynamic equations

Yıl 2021, , 77 - 86, 30.06.2021
https://doi.org/10.53006/rna.865900

Öz

In this work, we investigate the asymptotic stability of the zero solution for Caputo-Hadamard fractional dynamic equations on a time scale. We will make use of the Krasnoselskii fixed point theorem in a weighted Banach space to show new stability results.

Kaynakça

  • [1] M. Adivar, Y. N. Raffoul, Existence of periodic solutions in totally nonlinear delay dynamic equations, Electronic Journal of Qualitative Theory of Differential Equations 2009(1) (2009), 1--20.
  • [2] A. Ahmadkhanlu and M. Jahanshahi, On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales, Bull. Iranian Math. Soc. 38 (2012), no. 1, 241-252.
  • [3] R. P. Agarwal, M. Bohner, A. Peterson and D. O'Regan, Advances in Dynamic Equations on Time Scales, Birkhaurser, Boston, 2003.
  • [4] R. P. Agarwal, Y. Zhou, Y. He, Existence of fractional functional differential equations, Computers and Mathematics with Applications 59 (2010) 1095-1100.
  • [5] A. Ardjouni, I. Derrardjia and A. Djoudi, Stability in totally nonlinear neutral differential equations with variable delay, Acta Math. Univ. Comenianae, Vol. LXXXIII, 1 (2014), pp. 119-134.
  • [6] A. Ardjouni, A Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with functional delay on a time scale, Acta Univ. Palacki. Olomnc., Fac. rer. nat., Mathematica 52, 1 (2013) 5-19.
  • [7] A. Ardjouni, A Djoudi, Stability in neutral nonlinear dynamic equations on time scale with unbounded delay, Stud. Univ. Babeç-Bolyai Math. 57(2012), No. 4, 481-496.
  • [8] A. Ardjouni, A Djoudi, Fixed points and stability in linear neutral differential equations with variable delays, Nonlinear Analysis 74 (2011), 2062-2070.
  • [9] M. Belaid, A. Ardjouni, H. Boulares and A. Djoudi, Stability by Krasnoselskii's fixed point theorem for nonlinear fractional dynamic equations on a time scale, Honam Mathematical J. 41(1) (2019), 51--65.
  • [10] M. Belaid, A. Ardjouni and A. Djoudi, Stability in totally nonlinear neutral dynamic equations on time scales, International Journal of Analysis and Applications, Vol. 11, Nu. 2 (2016), 110-123.
  • [11] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhauser, Boston, 2001.
  • [12] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
  • [13] H. Boulares, A. Ardjouni, Y. Laskri, Positive solutions for nonlinear fractional differential equations, Positivity (2017) 21:1201--1212.
  • [14] H. Boulares, A. Ardjouni, Y. Laskri, Stability in delay nonlinear fractional differential equations, Rend. Circ. Mat. Palermo (2016) 65:243--253.
  • [15] I. Derrardjia, A. Ardjouni and A. Djoudi, Stability by Krasnoselskii's theorem in totally nonlinear neutral differential equations, Opuscula Math. 33(2) (2013), 255-272.
  • [16] M. Haoues, A. Ardjouni, A. Djoudi, Existence and uniqueness of solutions for the nonlinear retarded and advanced implicit Hadamard fractional differential equations with nonlocal conditions, Nonlinear studies 27(2) (2020), 433-445.
  • [17] M. Haoues, A. Ardjouni, A. Djoudi, Existence, uniqueness and monotonicity of positive solutions for hybrid fractional integro-di erential equations, Asia Mathematika 4(3) (2020), 1-13.
  • [18] Z. A. Khan, Hadamard-type fractional differential equations for the system of integral inequalities on time scales, Integral Transforms and Special Functions 31(1) (2020), 1-12.
  • [19] A. A. Kilbas, H. H. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V., Amsterdam, 2006.
  • [20] F. Ge, C. Kou, Stability analysis by Krasnoselskii's fixed point theorem for nonlinear fractional differential equations, Applied Mathematics and Computation 257 (2015) 308-316.
  • [21] F. Ge, C. Kou, Asymptotic stability of solutions of nonlinear fractional differential equations of order 1<a<2, Journal of Shanghai Normal University, Vol. 44, No. 3, 284-290.
  • [22] C. Kou, H. Zhou, Y. Yan, Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis, Nonlinear Anal. 74 (2011) 5975--5986.
  • [23] G. Liu, J. Yan, Global asymptotic stability of nonlinear neutral differential equation, Commun Nonlinear Sci Numer Simulat 19 (2014) 1035-1041.
  • [24] D. R. Smart, Fixed point theorems, Cambridge Tracts in Mathematics, no. 66, Cambridge University Press, London--New York, 1974.
  • [25] R. A. Yan, S. R. Sun and Han, Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales, Bull. Iranian Math. Soc., Vol. 42 (2016), No. 2, pp. 247-262.
Yıl 2021, , 77 - 86, 30.06.2021
https://doi.org/10.53006/rna.865900

Öz

Kaynakça

  • [1] M. Adivar, Y. N. Raffoul, Existence of periodic solutions in totally nonlinear delay dynamic equations, Electronic Journal of Qualitative Theory of Differential Equations 2009(1) (2009), 1--20.
  • [2] A. Ahmadkhanlu and M. Jahanshahi, On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales, Bull. Iranian Math. Soc. 38 (2012), no. 1, 241-252.
  • [3] R. P. Agarwal, M. Bohner, A. Peterson and D. O'Regan, Advances in Dynamic Equations on Time Scales, Birkhaurser, Boston, 2003.
  • [4] R. P. Agarwal, Y. Zhou, Y. He, Existence of fractional functional differential equations, Computers and Mathematics with Applications 59 (2010) 1095-1100.
  • [5] A. Ardjouni, I. Derrardjia and A. Djoudi, Stability in totally nonlinear neutral differential equations with variable delay, Acta Math. Univ. Comenianae, Vol. LXXXIII, 1 (2014), pp. 119-134.
  • [6] A. Ardjouni, A Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with functional delay on a time scale, Acta Univ. Palacki. Olomnc., Fac. rer. nat., Mathematica 52, 1 (2013) 5-19.
  • [7] A. Ardjouni, A Djoudi, Stability in neutral nonlinear dynamic equations on time scale with unbounded delay, Stud. Univ. Babeç-Bolyai Math. 57(2012), No. 4, 481-496.
  • [8] A. Ardjouni, A Djoudi, Fixed points and stability in linear neutral differential equations with variable delays, Nonlinear Analysis 74 (2011), 2062-2070.
  • [9] M. Belaid, A. Ardjouni, H. Boulares and A. Djoudi, Stability by Krasnoselskii's fixed point theorem for nonlinear fractional dynamic equations on a time scale, Honam Mathematical J. 41(1) (2019), 51--65.
  • [10] M. Belaid, A. Ardjouni and A. Djoudi, Stability in totally nonlinear neutral dynamic equations on time scales, International Journal of Analysis and Applications, Vol. 11, Nu. 2 (2016), 110-123.
  • [11] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhauser, Boston, 2001.
  • [12] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
  • [13] H. Boulares, A. Ardjouni, Y. Laskri, Positive solutions for nonlinear fractional differential equations, Positivity (2017) 21:1201--1212.
  • [14] H. Boulares, A. Ardjouni, Y. Laskri, Stability in delay nonlinear fractional differential equations, Rend. Circ. Mat. Palermo (2016) 65:243--253.
  • [15] I. Derrardjia, A. Ardjouni and A. Djoudi, Stability by Krasnoselskii's theorem in totally nonlinear neutral differential equations, Opuscula Math. 33(2) (2013), 255-272.
  • [16] M. Haoues, A. Ardjouni, A. Djoudi, Existence and uniqueness of solutions for the nonlinear retarded and advanced implicit Hadamard fractional differential equations with nonlocal conditions, Nonlinear studies 27(2) (2020), 433-445.
  • [17] M. Haoues, A. Ardjouni, A. Djoudi, Existence, uniqueness and monotonicity of positive solutions for hybrid fractional integro-di erential equations, Asia Mathematika 4(3) (2020), 1-13.
  • [18] Z. A. Khan, Hadamard-type fractional differential equations for the system of integral inequalities on time scales, Integral Transforms and Special Functions 31(1) (2020), 1-12.
  • [19] A. A. Kilbas, H. H. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V., Amsterdam, 2006.
  • [20] F. Ge, C. Kou, Stability analysis by Krasnoselskii's fixed point theorem for nonlinear fractional differential equations, Applied Mathematics and Computation 257 (2015) 308-316.
  • [21] F. Ge, C. Kou, Asymptotic stability of solutions of nonlinear fractional differential equations of order 1<a<2, Journal of Shanghai Normal University, Vol. 44, No. 3, 284-290.
  • [22] C. Kou, H. Zhou, Y. Yan, Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis, Nonlinear Anal. 74 (2011) 5975--5986.
  • [23] G. Liu, J. Yan, Global asymptotic stability of nonlinear neutral differential equation, Commun Nonlinear Sci Numer Simulat 19 (2014) 1035-1041.
  • [24] D. R. Smart, Fixed point theorems, Cambridge Tracts in Mathematics, no. 66, Cambridge University Press, London--New York, 1974.
  • [25] R. A. Yan, S. R. Sun and Han, Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales, Bull. Iranian Math. Soc., Vol. 42 (2016), No. 2, pp. 247-262.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Abdelouaheb Ardjouni

Yayımlanma Tarihi 30 Haziran 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Ardjouni, A. (2021). Asymptotic stability in Caputo-Hadamard fractional dynamic equations. Results in Nonlinear Analysis, 4(2), 77-86. https://doi.org/10.53006/rna.865900
AMA Ardjouni A. Asymptotic stability in Caputo-Hadamard fractional dynamic equations. RNA. Haziran 2021;4(2):77-86. doi:10.53006/rna.865900
Chicago Ardjouni, Abdelouaheb. “Asymptotic Stability in Caputo-Hadamard Fractional Dynamic Equations”. Results in Nonlinear Analysis 4, sy. 2 (Haziran 2021): 77-86. https://doi.org/10.53006/rna.865900.
EndNote Ardjouni A (01 Haziran 2021) Asymptotic stability in Caputo-Hadamard fractional dynamic equations. Results in Nonlinear Analysis 4 2 77–86.
IEEE A. Ardjouni, “Asymptotic stability in Caputo-Hadamard fractional dynamic equations”, RNA, c. 4, sy. 2, ss. 77–86, 2021, doi: 10.53006/rna.865900.
ISNAD Ardjouni, Abdelouaheb. “Asymptotic Stability in Caputo-Hadamard Fractional Dynamic Equations”. Results in Nonlinear Analysis 4/2 (Haziran 2021), 77-86. https://doi.org/10.53006/rna.865900.
JAMA Ardjouni A. Asymptotic stability in Caputo-Hadamard fractional dynamic equations. RNA. 2021;4:77–86.
MLA Ardjouni, Abdelouaheb. “Asymptotic Stability in Caputo-Hadamard Fractional Dynamic Equations”. Results in Nonlinear Analysis, c. 4, sy. 2, 2021, ss. 77-86, doi:10.53006/rna.865900.
Vancouver Ardjouni A. Asymptotic stability in Caputo-Hadamard fractional dynamic equations. RNA. 2021;4(2):77-86.

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