In this study, we present a generalized concept of Seikkala differentiability for fuzzy functions. It has been shown that this concept and the lateral H-differentiability lead us to the same results. Fuzzy differential transform method (FDTM) is applied to solve fuzzy Volterra integro-differential equations. In order to show the effectiveness of this method some illustrative examples are given.
MizukoshiM.T., BarrosL.C., Chalco-CanoY., Roman-FloresH. and BassaneziR.C., Fuzzy differential equations and extension principle, Information Sciences177 (2007), 3627–3635.
2.
PuriM. and RalescuD., Differentials of fuzzy functions, J Math Anal Appl91 (1983), 552–558.
3.
SeikkalaS., On the fuzzy initial value problem, Fuzzy and Systems24 (1987), 319–330.
4.
BabolianE., SadeghiGogharyH. and AbbasbandyS., Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method, Applied Mathematics and Computation161 (2005), 733–744.
5.
Chalco-CanoY. and Romn-FloresH., On new solutions of fuzzy differential equations, Chaos, Solitons and Fractals38 (2008), 112–119.
6.
BedeB., Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, 2013, pp. 157–158.
7.
SalahshourS. and AllahviranlooT., Application of fuzzy differential transform method for solving fuzzy Volterra integral equations, Applied Mathematical Modelling37 (2013), 1016–1027.
8.
ZadehL., Toward a generalized theory of uncertainty (GTU) – an outline, Information Sciences175 (2005), 1–40.
9.
CasasnovasJ. and RossellF., Averaging fuzzy biopolymers, Fuzzy Sets and Syst152 (2005), 139–158.
10.
BarrosL.C., BassaneziR.C. and TonelliP.A., Fuzzy modelling in population dynamics, Ecol Model128 (2000), 27–33.
11.
El NaschieM.S., From experimental quantum optics to quantum gravity via a fuzzy Khler Manifold, Chaos, Solitons and Fractals25 (2005), 969–977.
12.
BarrosL.C. and PedroF.S., Fuzzy differential equations with interactive derivative, Fuzzy Sets and Systems309 (2017), 64–80.
13.
SubrahmanyamP.V. and SudarsanamS.K., A note on fuzzy Volterra integral equations, Fuzzy Sets and Systems81 (1996), 237–240.
14.
BedeB. and GalS.G., Generalizations of differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems151 (2005), 581–599.
15.
ZhouJ.K., Differential Transformation and its application for electrical circuits, Huazhong University Press, Wuhan, China, 1986.
16.
BedeB. and StefaniniL., Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis71 (2009), 1311–1328.
17.
BedeB. and StefaniniL., Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems230 (2013), 119–141.
18.
BedeB. and GalS.G., Quadrature rules for integrals of fuzzy-number-valued functions, Fuzzy Sets Syst145 (2004), 359–380.
19.
MoslehM. and OtadiM., Existence of solution of nonlinear fuzzy Fredholm integro-differential equations, Fuzzy Information and Engineering8 (2016), 17–30.
20.
ZeinaliM., ShahmoradS. and MirniaK., Fuzzy intrego-differential equations: Discrete solution and error estimation, Iranian Journal of Fuzzy Systems10 (2013), 107–122.
21.
MirzaeeF. and HoseiniS.F., Solving systems of linear Fredholm integro-differential equations with Fibonacci polynomials, Ain Shams Engineering Journal5 (2014), 271–283.
22.
AlikhaniR., BahramiF. and JabbariA., Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations, Nonlin Anal75 (2012), 1810–1821.
23.
AttariH. and YazdaniA., A computational method for fuzzy Volterra Fredholm integral equations, Fuzzy Inf Eng2 (2011), 147–156.
24.
Khorasani KiasariS.M., KhezerlooM., Dogani AghcheghlooM.H., Numerical solution of Linear Fredholm fuzzy integral equations by modified homotopy perturbation method, Aust J Basic Appl Sci4 (2010), 6416–6423.
25.
MolabahramiA., ShidfarA. and GhyasiA., Ananalytical method for solving linear Fredholm fuzzy integral equations of the second kind, Comput Math Appl61 (2011), 2754–2761.
26.
AbbasbandyS., BabolianE. and AlaviM., Numerical method for solving linear Fredholm fuzzy Integral equations of the second kind, Chaos Solitons Fractals31(1) (2007), 138–146.
27.
MatinfarM., GhanbariM. and NuraeiR., Numerical solution of linear fuzzy Volterra integro-differential equations by variational iteration method, Journal of Intelligent & Fuzzy Systems24 (2013), 575–586.
28.
AllahviranlooT., AbbasbandyS., SedaghatfarO. and DarabiP., A new method for solving fuzzy integro-differential equation under generalized differentiability, Neural Computing and Applications21 (2012), 191–196.
29.
BehzadiS.S., AllahviranlooT. and AbbasbandyS., Fuzzy collocation methods for second-order fuzzy Abel-Volterra integro-differential equations, Iranian Journal of Fuzzy Systems11(2) (2014), 71–88.
30.
AllahviranlooT., AmirteimooriA., KhezerlooM. and KhezerlooS., A new method for solving fuzzy Voltra integro-differential equations, Journal of Australian Journal of Basic and Applied Sciences5(4) (2011), 154–164.
31.
BehzadiSh.S., AllahviranlooT. and AbbasbandyS., Solving fuzzy second-order nonlinear Volterra–Fredholm integro-differential equations by using Picard method, Journal of Neural Computing & Applications21(1) (2012), 337–346.
32.
DiamondP., Stability and periodicity in fuzzy differential equations, IEEE Transactions on Fuzzy Systems8 (2000), 583–590.
33.
Chalco-CanoY. and Roman-FloresH., Comparation between some approaches to solve fuzzy differential equations, Fuzzy Sets and Systems160 (2009), 1517–1527.