| Title of paper:
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Intuitionistic fuzzy fractional boundary value problem
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| Author(s):
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| Said Melliani
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| Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
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| said.melliani@gmail.com
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| M. Elomari
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| Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
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| A. Elmfadel
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| Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
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| Presented at:
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4th International Intuitionistic Fuzzy Sets and Contemporary Mathematics Conference, 3–7 May 2017, Mersin, Turkey
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 23, 2017, Number 1, pages 31—41
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| Download:
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 PDF (157 Kb Kb, File info)
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| Abstract:
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In this paper we investigate the existence and uniquness of intuitionistic fuzzy solution for three-point boundary value problem for fractional differential equation:
[math]\displaystyle{ \left\{ \begin{array}{lrr}
D^{\alpha}X(t)=F(t, X_t, D^{\beta}X(t)) & t\in J:=[0, 1]\\
X(t)=\phi(t)&t\in[-r, 0]\\
X(1)=X(\xi)&
\end{array}, \right.
}[/math]
where [math]\displaystyle{ D^{\alpha}, D^{\beta} }[/math] are the standard Riemann--Liouville fractional derivatives (α−β>0) and (1<α < 2), [math]\displaystyle{ (\xi\in[0, 1[) }[/math],[math]\displaystyle{ F:J \times C_0\times\mathbf{IF}^1 \longrightarrow \mathbf{IF}^1 }[/math] is an intuitionistic fuzzy function, [math]\displaystyle{ \phi\in C_0 }[/math], [math]\displaystyle{ \phi(0)=0_{IF} }[/math] and [math]\displaystyle{ C_0=C\left([-r, 0], IF^1\right) }[/math]. We denote by [math]\displaystyle{ X_t }[/math] the element of [math]\displaystyle{ C_0 }[/math] defined by [math]\displaystyle{ X_t(\theta)=X(t+\theta) }[/math], [math]\displaystyle{ \theta\in[-r, 0]. }[/math]
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| Keywords:
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Intuitionistic fuzzy sets, Distance between intuitionistic fuzzy sets, Intuitionistic fractional derivative.
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| AMS Classification:
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03E72.
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| References:
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- Bede, B., & Gal, S. G. (2005). Generalizations of the differentiability of fuzzy-numbervalued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems, 151, 581–599.
- Kilbas, A. A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and Applications of Fractional Sifferential Equations, North-Holland Mathematical studies 204, Ed van Mill, Amsterdam.
- Melliani, S., Elomari, M. Chadli, L. S., & Ettoussi, R. (2015). Intuitionistic fuzzy metric space, Notes on Intuitionistic Fuzzy Sets, 21(1), 43–53.
- Salahshour, S., Allahviranloo, T., Abbasbandy, S., & Baleanu, D. (2012). Existence and uniqueness results for fractional differential equations with uncertainty. Adv. Diff. Equ., 112, doi:10.1186/1687-1847-2012-112.
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