In this paper, we discuss two point boundary value problems of second-order fuzzy boundary value problem. Using monotone iterative method, we investigate the existence of solutions to boundary value problem of fuzzy integro-differential equation firstly, then the results are applied to discuss second-order fuzzy boundary value problem.
BarrosL.C., BassaneziR.C., TonelliP.A.Fuzzy modelling in population dynamics, Ecological Modelling128 (2000), 27–33.
2.
LakshmikanthamV., MohapatraR.N.Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis, 2003.
3.
KhastanA.New solutions for first order linear fuzzy difference equations, Journal of Computational and Applied Mathematics312 (2017), 156–166.
4.
Macias-DiazJ.E., TomasielloS., A differential quadraturebased approach a la Picard for systems of partial differential equations associated with fuzzy differential equations, Journal of Computational and Applied Mathematics299 (2016), 15–23.
5.
ChenM., LiD., XueX., Periodic problems of first order uncertain dynamical systems, Fuzzy Sets and Systems162 (2011), 67–78.
6.
LongH.V., SonN.T.K., HaN.T.M., SonL.H., The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations, Fuzzy Optimization and Decision Making13 (2014), 435–462.
7.
AlikhaniR., BahramiF., JabbariA., Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations, Nonlinear Analysis75 (2012), 1810–1821.
8.
AlikhaniR., BahramiF., Global solutions of fuzzy integrodifferential equations under generalized differentiability by the method of upper and lower solutions, Information Sciences295 (2015), 600–608.
9.
Rodriguez-LopezR., Monotone method for fuzzy differential equations, Fuzzy Sets and Systems159 (2008), 2047–2076.
10.
ChenM., WuC., XueX., On fuzzy boundary value problems, Information Sciences178 (2008), 1877–1892.
11.
LiD., ChenM., XueX., Two-point boundary value problems of uncertain dynamical systems, Fuzzy Sets and Systems179 (2011), 50–61.
12.
KhastanA., NietoJ.J., Rodriguez-LopezR., Periodic boubdary value problems for first-order linear differential equations with uncertainty under generalized differentiability, Information Sciences222 (2013), 544–558.
13.
NietoJ.J., Rodriguez-LopezR., Villanueva-PesqueiraM., Exact solution to the periodic boundary value problem for a firstorder linear fuzzy differential equation with impulses, Fuzzy Optimization and Decision Making10 (2011), 323–339.
14.
Rodriguez-LopezR., On the existence of solutions to periodic boundary value problems for fuzzy linear differential equations, Fuzzy Sets and Systems219 (2013), 1–26.
15.
NietoJ.J., Rodriguez-LopezR., Some results on boundary value problems for fuzzy differential equations with functional dependence, Fuzzy Sets and Systems230 (2013), 92–118.
16.
KhastanA., NietoJ.J., A boundary value problem for second order fuzzy differential equations, Nonlinear Analysis72 (2010), 3583–3593.
17.
LakshmikanthamV., MurtyK.N., TurnerJ., Two-point boundary value problems associated with nonlinear fuzzy differential equations, Mathematical Inequalities and Applications4 (2001), 527–533.
18.
O’ReganD., LakshmikanthamV., NietoJ., Initial and boundary value problems for fuzzy differential equations, Nonlinear Analysis54 (2003), 405–415.
19.
BedeB., A note on “two-point boundary value problems associated with non-linear fuzzy differential equations”, Fuzzy Sets and Systems157 (2006), 986–989.
20.
WangH., Monotone iterative method for boundary value problems of fuzzy differential equations, Journal of Intelligent and Fuzzy Systems30 (2016), 831–843.
21.
BedeB., RudasI.J., BencsikA.L., First order linear fuzzy differentail equations under generalized differentiability, Information Sciences177 (2007), 1648–1662.
22.
PuriM., RalescuD., Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications91 (1983), 552–558.
23.
WuC., GongZ., On Henstock integral of fuzzy-number-valued functions (I), Fuzzy Sets and Systems120 (2001), 523–532.
24.
Rodriguez-LopezR., Comparison results for fuzzy differential equations, Information Sciences178 (2008), 1756–1779.
25.
AllahviranlooT., ArmandA., GouyandehZ., Fuzzy fractional differential equations under generalized fuzzy Caputo derivative, Journal of Intelligent and Fuzzy Systems26 (2014), 1481–1490.
26.
AllahviranlooT., AhmadyN., AhmadyE., Improved predictor-corrector method for solving fuzzy initial value problems, Information Sciences179 (2009), 945–955.
27.
SalahshourS., AllahviranlooT., Application of fuzzy differential transform method for solving fuzzy Volterra integral equations, Applied Mathematical Modelling37 (2013), 1016–1027.
28.
AbbasbandyS., AllahviranlooT., The Adomian decomposition method applied to the Fuzzy system of Fredholm integral equations of the second kind, International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems14 (2006), 101–110.