Research Article
Year 2018,
Volume: 1 Issue: 2, 155 - 165, 31.07.2018
Abstract
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.
Keywords
References
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- 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).
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- 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.
Year 2018,
Volume: 1 Issue: 2, 155 - 165, 31.07.2018
Abstract
References
- 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.
There are 14 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | July 31, 2018 |
| Submission Date | May 15, 2018 |
| Acceptance Date | August 5, 2018 |
| Published in Issue | Year 2018 Volume: 1 Issue: 2 |
