Araştırma Makalesi
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CONTROLLED FUZZY EVOLUTION EQUATIONS

Yıl 2018, Cilt: 1 Sayı: 2, 155 - 165, 31.07.2018

Öz

This paper is concerned with controlled fuzzy nonlinear evolution equations of the form u'(t) = Au(t) + f(t, u(t), u(rho((t)) + B(t)c(t); t in [t_0; t_1] and u(t_0) = u_0. Where c(t) is a fuzzy control, the operator A generate a fuzzy semigroup. We use the fuzzy strongly continuous semigroups theory to prove the existence, uniqueness and some properties of mild solutions.

Kaynakça

  • R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl., (1965), 1-12.
  • A. El Allaoui, S. Melliani and L. S. Chadli, Fuzzy dynamical systems and Invariant attractor sets for fuzzy strongly continuous semigroups, Journal of Fuzzy Set Valued Analysis 2016 No.2 (2016) 148-155.
  • A. El Allaoui, S. Melliani, L. S. Chadli, Fuzzy alpha-semigroups of operators, General Letters in Mathematics Vol 2 (2) (2017) 42-49.
  • Bhaskar Dubey, Raju K. George, Controllability of Linear Time-invariant Dynamical Systems with Fuzzy Initial Condition, Proceedings of the World Congress on Engineering and Computer Science (2013), 23-25.
  • Bhaskar Dubey and Raju K. George, Estimation of controllable initial fuzzy states of linear time-invariant dynamical systems, Communications in Computer and Information Science, Springer, (2012), 316-324.
  • Y. Feng, L. Hua, On the quasi-controllability of continuous-time dynamic fuzzy control systems, Chaos, Solitons & Fractals (2006), 177-188.
  • C. G. Gal and S. G. Gal, Semigroups of Operators on Spaces of Fuzzy-Number-Valued Functions with Applications to Fuzzy Differential Equations, arXiv:1306.3928v1 (2013).
  • M. Hukuhara, Integration des applications measurables dont la valeur est un compact convexe, Funk. Ekvacioj (1967), 207-223.
  • O. Kaleva, Fuzzy Differentiel Equations, Fuzzy Sets and Systems. (1987), 24: 301{317.
  • Said Melliani, El Hassan Eljaoui and Lalla Saadia Chadli, Fuzzy Differential Equation With Nonlocal Conditions And Fuzzy semigroups, Advances in Difference Equations (2016).
  • S. Melliani, L. S. Chadli, A. El Allaoui, Periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces. International Journal of Nonlinear Analy-sis and Applications, 8(1) (2017), 301-314.
  • S. Melliani, A. El Allaoui and L. S. Chadli, A general classof periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces, Advances in Difference Equations (2016): 290.
  • S. Melliani, A. El Allaoui and L. S. Chadli , Relation Between Fuzzy Semigroups and Fuzzy Dynamical Systems, Nonlinear Dynamics and Systems Theory, 17 (1) (2017) 60-69.
  • M. L. Puri, D. A. Ralescu. Fuzzy random variables, J. Math. Anal. Appl. (1986), 114: 409-422.
Yıl 2018, Cilt: 1 Sayı: 2, 155 - 165, 31.07.2018

Öz

Kaynakça

  • R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl., (1965), 1-12.
  • A. El Allaoui, S. Melliani and L. S. Chadli, Fuzzy dynamical systems and Invariant attractor sets for fuzzy strongly continuous semigroups, Journal of Fuzzy Set Valued Analysis 2016 No.2 (2016) 148-155.
  • A. El Allaoui, S. Melliani, L. S. Chadli, Fuzzy alpha-semigroups of operators, General Letters in Mathematics Vol 2 (2) (2017) 42-49.
  • Bhaskar Dubey, Raju K. George, Controllability of Linear Time-invariant Dynamical Systems with Fuzzy Initial Condition, Proceedings of the World Congress on Engineering and Computer Science (2013), 23-25.
  • Bhaskar Dubey and Raju K. George, Estimation of controllable initial fuzzy states of linear time-invariant dynamical systems, Communications in Computer and Information Science, Springer, (2012), 316-324.
  • Y. Feng, L. Hua, On the quasi-controllability of continuous-time dynamic fuzzy control systems, Chaos, Solitons & Fractals (2006), 177-188.
  • C. G. Gal and S. G. Gal, Semigroups of Operators on Spaces of Fuzzy-Number-Valued Functions with Applications to Fuzzy Differential Equations, arXiv:1306.3928v1 (2013).
  • M. Hukuhara, Integration des applications measurables dont la valeur est un compact convexe, Funk. Ekvacioj (1967), 207-223.
  • O. Kaleva, Fuzzy Differentiel Equations, Fuzzy Sets and Systems. (1987), 24: 301{317.
  • Said Melliani, El Hassan Eljaoui and Lalla Saadia Chadli, Fuzzy Differential Equation With Nonlocal Conditions And Fuzzy semigroups, Advances in Difference Equations (2016).
  • S. Melliani, L. S. Chadli, A. El Allaoui, Periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces. International Journal of Nonlinear Analy-sis and Applications, 8(1) (2017), 301-314.
  • S. Melliani, A. El Allaoui and L. S. Chadli, A general classof periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces, Advances in Difference Equations (2016): 290.
  • S. Melliani, A. El Allaoui and L. S. Chadli , Relation Between Fuzzy Semigroups and Fuzzy Dynamical Systems, Nonlinear Dynamics and Systems Theory, 17 (1) (2017) 60-69.
  • M. L. Puri, D. A. Ralescu. Fuzzy random variables, J. Math. Anal. Appl. (1986), 114: 409-422.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Said Melliani 0000-0002-5150-1185

Abdelati El Allaoui Bu kişi benim

Lalla Saadia Chadli

Yayımlanma Tarihi 31 Temmuz 2018
Gönderilme Tarihi 15 Mayıs 2018
Kabul Tarihi 5 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

APA Melliani, S., El Allaoui, A., & Chadli, L. S. (2018). CONTROLLED FUZZY EVOLUTION EQUATIONS. Journal of Universal Mathematics, 1(2), 155-165.
AMA Melliani S, El Allaoui A, Chadli LS. CONTROLLED FUZZY EVOLUTION EQUATIONS. JUM. Temmuz 2018;1(2):155-165.
Chicago Melliani, Said, Abdelati El Allaoui, ve Lalla Saadia Chadli. “CONTROLLED FUZZY EVOLUTION EQUATIONS”. Journal of Universal Mathematics 1, sy. 2 (Temmuz 2018): 155-65.
EndNote Melliani S, El Allaoui A, Chadli LS (01 Temmuz 2018) CONTROLLED FUZZY EVOLUTION EQUATIONS. Journal of Universal Mathematics 1 2 155–165.
IEEE S. Melliani, A. El Allaoui, ve L. S. Chadli, “CONTROLLED FUZZY EVOLUTION EQUATIONS”, JUM, c. 1, sy. 2, ss. 155–165, 2018.
ISNAD Melliani, Said vd. “CONTROLLED FUZZY EVOLUTION EQUATIONS”. Journal of Universal Mathematics 1/2 (Temmuz 2018), 155-165.
JAMA Melliani S, El Allaoui A, Chadli LS. CONTROLLED FUZZY EVOLUTION EQUATIONS. JUM. 2018;1:155–165.
MLA Melliani, Said vd. “CONTROLLED FUZZY EVOLUTION EQUATIONS”. Journal of Universal Mathematics, c. 1, sy. 2, 2018, ss. 155-6.
Vancouver Melliani S, El Allaoui A, Chadli LS. CONTROLLED FUZZY EVOLUTION EQUATIONS. JUM. 2018;1(2):155-6.