Hybrid fuzzy differential equations

Atimad Harir; Said Melliani; L. Saadia Chadli; Atimad Harir; Said Melliani; L. Saadia Chadli

doi:10.3934/math.2020018

AIMS Mathematics

2020, Volume 5, Issue 1: 273-285. doi: 10.3934/math.2020018

Previous Article Next Article

Review

Hybrid fuzzy differential equations

Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, P. O. Box 523, Beni Mellal, 23000, Morocco

Received: 27 July 2019 Accepted: 31 October 2019 Published: 07 November 2019
MSC : 03E72, 34A12, 46S40

In this paper we study the existence of the solution for a class of hybrid differential equations with fuzzy initial value. The some new results of generalized division are proposed and applied.
- hybrid differential equation,
- fuzzy initial value,
- generalized division,
- fuzzy solution
Citation: Atimad Harir, Said Melliani, L. Saadia Chadli. Hybrid fuzzy differential equations[J]. AIMS Mathematics, 2020, 5(1): 273-285. doi: 10.3934/math.2020018

Related Papers:

Abstract

In this paper we study the existence of the solution for a class of hybrid differential equations with fuzzy initial value. The some new results of generalized division are proposed and applied.

References

[1]	R. Boukezzoula, S. Galichet, L. Foulloy, Inverse arithmetic operators for fuzzy intervals, In: Proc. EUSFLAT 2007 Conf., Ostrawa, 279-286.
[2]	L. S. Chadli, A. Harir, S. Melliani, Fuzzy Euler differential equation, SOP Trans. Appl. Math., 2 (2015).
[3]	L. S. Chadli, A. Harir, S. Melliani, Solutions of fuzzy heat-like equations by variational iterative method, Ann. Fuzzy Math. Inf., 10 (2015), 29-44.
[4]	L. S. Chadli, A. Harir, S. Melliani, Solutions of fuzzy wave-like equations by variational iteration method, Int. Ann. Fuzzy Math. Inf., 8 (2014), 527-547.
[5]	B. C. Dhage, D. O'Regan, A fixed point theorem in Banach algebras with applications to functional integral equations, Funct. Differ. Eq., 7 (2004), 259-267.
[6]	B. C. Dhage, On α-condensing mappings in Banach algebras, Math. Student, 63 (1994), 146-152.
[7]	B. C. Dhage, V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Anal. Hybrid syst., 4 (2010), 414-424. doi: 10.1016/j.nahs.2009.10.005
[8]	B. C. Dhage, A nonlinear alternative in Banach algebras with applications to functional differential equations, Nonlinear Funct. Anal. Appl., 8 (2004), 563-575.
[9]	D. Qiu, C. Lu, W. Hhang, et al. Algebraic properties and topological properties of the quotient space of fuzzy numbers based on Mares equivalence relation, Fuzzy set. Syst., 245 (2014), 63-82. doi: 10.1016/j.fss.2014.01.003
[10]	D. Qiu, W. Hhang, C. Lu, On fuzzy differential equations in the quotient space of fuzzy numbers, Fuzzy set. Syst., 295 (2016), 72-98. doi: 10.1016/j.fss.2015.03.010
[11]	O. Kaleva, Fuzzy differential equations, Fuzzy Set. Syst., 24 (1987), 301-317. doi: 10.1016/0165-0114(87)90029-7
[12]	M. Ma, M. Friedman, A. Kandel, A new fuzzy arithmetic, Fuzzy Set. Syst., 108 (1999), 83-90. doi: 10.1016/S0165-0114(97)00310-2
[13]	S. Seikkala, On the fuzzy initialvalue problem, Fuzzy Set. Syst., 24 (1987), 319-330. doi: 10.1016/0165-0114(87)90030-3
[14]	L. Stefanini, Ageneralization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Set. Syst., 161 (2010), 1564-1584. doi: 10.1016/j.fss.2009.06.009

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)