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Volumn 18, Issue 11, 2014, Pages 2191-2200

Solving nonlinear fuzzy differential equations by using fuzzy variational iteration method

Author keywords

Fuzzy differential equations; Fuzzy number; Fuzzy variational iteration method (FVIM); Fuzzy valued function; Generalized differentiability; gh difference; h difference

Indexed keywords

DIFFERENTIAL EQUATIONS; FUZZY SETS; ITERATIVE METHODS;

EID: 84919443111     PISSN: 14327643     EISSN: 14337479     Source Type: Journal    
DOI: 10.1007/s00500-013-1193-5     Document Type: Article
Times cited : (19)

References (55)
  • 1
    • 85000083726 scopus 로고    scopus 로고
    • Numerical solutions of fuzzy differential equations by Taylor method
    • Abbasbandy S, Allahviranloo T (2002) Numerical solutions of fuzzy differential equations by Taylor method. J Comput Methods Appl Math 2:113–124
    • (2002) J Comput Methods Appl Math , vol.2 , pp. 113-124
    • Abbasbandy, S.1    Allahviranloo, T.2
  • 3
    • 20444443902 scopus 로고    scopus 로고
    • Tuning of reachable set in one dimensional fuzzy differential inclusions
    • Abbasbandy S, Nieto JJ, Alavi M (2005) Tuning of reachable set in one dimensional fuzzy differential inclusions. Chaos Solitons Fract 26:1337
    • (2005) Chaos Solitons Fract , vol.26 , pp. 1337
    • Abbasbandy, S.1    Nieto, J.J.2    Alavi, M.3
  • 5
    • 13544261423 scopus 로고    scopus 로고
    • The Adomian decomposition method for fuzzy system of linear equations
    • Allahviramloo T (2005) The Adomian decomposition method for fuzzy system of linear equations. Appl Math Comput 163:553– 563
    • (2005) Appl Math Comput , vol.163 , pp. 553-563
    • Allahviramloo, T.1
  • 6
    • 33846370208 scopus 로고    scopus 로고
    • Numerical solution of fuzzy differential equations by predictor–corrector method
    • Allahviranloo T, Ahmady N, Ahmady E (2007) Numerical solution of fuzzy differential equations by predictor–corrector method. Inf Sci 177:1633–1647
    • (2007) Inf Sci , vol.177 , pp. 1633-1647
    • Allahviranloo, T.1    Ahmady, N.2    Ahmady, E.3
  • 8
    • 38649113250 scopus 로고    scopus 로고
    • Note on numerical solutions of fuzzy differential equations by predictor–corrector method
    • Bede B (2008) Note on numerical solutions of fuzzy differential equations by predictor–corrector method. Inf Sci 178:1917– 1922
    • (2008) Inf Sci , vol.178 , pp. 1917-1922
    • Bede, B.1
  • 9
    • 14544296605 scopus 로고    scopus 로고
    • Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equation
    • Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equation. Fuzzy Set Syst 151:581–599
    • (2005) Fuzzy Set Syst , vol.151 , pp. 581-599
    • Bede, B.1    Gal, S.G.2
  • 10
    • 33846224330 scopus 로고    scopus 로고
    • First order linear fuzzy differential equations under generalized differentiability
    • Bede B, Imre J, Rudas C, Attila L (2007) First order linear fuzzy differential equations under generalized differentiability. Inf Sci 177:3627–3635
    • (2007) Inf Sci , vol.177 , pp. 3627-3635
    • Bede, B.1    Imre, J.2    Rudas, C.3    Attila, L.4
  • 11
    • 0012838528 scopus 로고    scopus 로고
    • Fuzzy differential equations
    • Buckley JJ, Feuring T (2000) Fuzzy differential equations. Fuzzy Set Syst 110:43–54
    • (2000) Fuzzy Set Syst , vol.110 , pp. 43-54
    • Buckley, J.J.1    Feuring, T.2
  • 13
    • 33750376265 scopus 로고    scopus 로고
    • Linear systems of first order ordinary differential equations: fuzzy initial conditions
    • Buckley JJ, Feuring T, Hayashi Y (2002) Linear systems of first order ordinary differential equations: fuzzy initial conditions. Soft Comput 6:415–421
    • (2002) Soft Comput , vol.6 , pp. 415-421
    • Buckley, J.J.1    Feuring, T.2    Hayashi, Y.3
  • 14
    • 58349109906 scopus 로고    scopus 로고
    • On new solutions of fuzzy differential Buckley and Jowers equations
    • Chalco-Cano Y, Romn-Flores H (2006) On new solutions of fuzzy differential Buckley and Jowers equations. Chaos Solitons Fract: 1016–1043
    • (2006) Chaos Solitons Fract , pp. 1016-1043
    • Chalco-Cano, Y.1    Romn-Flores, H.2
  • 16
    • 79953282911 scopus 로고    scopus 로고
    • Generalized derivative and π-derivative for set-valued functions
    • Chalco-Cano Y, Roman-Flores H, Jimnez-Gamero MD (2011) Generalized derivative and $$\pi $$π-derivative for set-valued functions. Inf Sci 181:2177–2188
    • (2011) Inf Sci , vol.181 , pp. 2177-2188
    • Chalco-Cano, Y.1    Roman-Flores, H.2    Jimnez-Gamero, M.D.3
  • 17
    • 0006035689 scopus 로고    scopus 로고
    • Solving partial differential equations by two-dimensional differential transform method
    • Chen CK, Ho SH (1999) Solving partial differential equations by two-dimensional differential transform method. Appl Math Comput 106:171–179
    • (1999) Appl Math Comput , vol.106 , pp. 171-179
    • Chen, C.K.1    Ho, S.H.2
  • 18
    • 37349008528 scopus 로고    scopus 로고
    • The existence of solutions for the nonlinear first order fuzzy differential equations with discontinuous conditions
    • Cho YJ, Lan HY (2007) The existence of solutions for the nonlinear first order fuzzy differential equations with discontinuous conditions. Dyn Contin Discrete 14:873–884
    • (2007) Dyn Contin Discrete , vol.14 , pp. 873-884
    • Cho, Y.J.1    Lan, H.Y.2
  • 19
    • 0032116380 scopus 로고
    • Exitance theorem to the Cauchy problem of fuzzy differential equations under compactance-type conditions
    • Congxin W, Shiji S (1993) Exitance theorem to the Cauchy problem of fuzzy differential equations under compactance-type conditions. Inf Sci 108:123–134
    • (1993) Inf Sci , vol.108 , pp. 123-134
    • Congxin, W.1    Shiji, S.2
  • 20
    • 0037411687 scopus 로고    scopus 로고
    • The golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology
    • Datta DP (2003) The golden mean, scale free extension of real number system, fuzzy sets and $$1/f$$1/f spectrum in physics and biology. Chaos Solitons Fract 17:781–788
    • (2003) Chaos Solitons Fract , vol.17 , pp. 781-788
    • Datta, D.P.1
  • 21
    • 0033281106 scopus 로고    scopus 로고
    • Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations
    • Diamond P (1999) Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations. IEEE Trans Fuzzy Syst 7:734–740
    • (1999) IEEE Trans Fuzzy Syst , vol.7 , pp. 734-740
    • Diamond, P.1
  • 22
    • 0036642870 scopus 로고    scopus 로고
    • Brief note on the variation of constants formula for fuzzy differential equations
    • Diamond P (2002) Brief note on the variation of constants formula for fuzzy differential equations. Fuzzy Set Syst 129:65–71
    • (2002) Fuzzy Set Syst , vol.129 , pp. 65-71
    • Diamond, P.1
  • 23
    • 0031189750 scopus 로고    scopus 로고
    • Existence of solutions of fuzzy differential equations with parameters
    • Ding Z, Ma M, Kandel A (1997) Existence of solutions of fuzzy differential equations with parameters. Inf Sci 99:205–217
    • (1997) Inf Sci , vol.99 , pp. 205-217
    • Ding, Z.1    Ma, M.2    Kandel, A.3
  • 25
    • 0020184062 scopus 로고
    • Towards fuzzy differential calculus: Part 3, differentiation
    • Dubois D, Prade H (1982) Towards fuzzy differential calculus: Part 3, differentiation. Fuzzy Set Syst 8:225–233
    • (1982) Fuzzy Set Syst , vol.8 , pp. 225-233
    • Dubois, D.1    Prade, H.2
  • 26
    • 18444404944 scopus 로고    scopus 로고
    • From experimental quantum optics to quantum gavity via a fuzzy Kahler manifold
    • El Naschie MS (2005) From experimental quantum optics to quantum gavity via a fuzzy Kahler manifold. Chaos Solitons Fract 25: 969–977
    • (2005) Chaos Solitons Fract , vol.25 , pp. 969-977
    • El Naschie, M.S.1
  • 27
    • 79960564734 scopus 로고    scopus 로고
    • A numerical scheme for fuzzy cauchy problems
    • Fard OS (2009a) A numerical scheme for fuzzy cauchy problems. J Uncertain Syst 3:307–314
    • (2009) J Uncertain Syst , vol.3 , pp. 307-314
    • Fard, O.S.1
  • 28
    • 79960565071 scopus 로고    scopus 로고
    • An iterative scheme for the solution of generalized system of linear fuzzy differential equations
    • Fard OS (2009b) An iterative scheme for the solution of generalized system of linear fuzzy differential equations. World Appl Sci J 7:1597–1604
    • (2009) World Appl Sci J , vol.7 , pp. 1597-1604
    • Fard, O.S.1
  • 29
    • 79955026678 scopus 로고    scopus 로고
    • Modified k-step method for solving fuzzy initial value problems
    • Fard OS, Kamyad AV (2011) Modified k-step method for solving fuzzy initial value problems. Iran J Fuzzy Syst 8(3):49–63
    • (2011) Iran J Fuzzy Syst , vol.8 , Issue.3 , pp. 49-63
    • Fard, O.S.1    Kamyad, A.V.2
  • 30
    • 79960564015 scopus 로고    scopus 로고
    • A note on iterative method for solving fuzzy initial value problems
    • Fard OS, Hadi Z, Ghal-Eh N, Borzabadi AH (2009) A note on iterative method for solving fuzzy initial value problems. J Adv Res Sci Comput 1:22–33
    • (2009) J Adv Res Sci Comput , vol.1 , pp. 22-33
    • Fard, O.S.1    Hadi, Z.2    Ghal-Eh, N.3    Borzabadi, A.H.4
  • 31
    • 79960561191 scopus 로고    scopus 로고
    • Approximate-analytical approach to nonlinear FDEs under generalized differentiability
    • Fard OS, Bidgoli TA, Borzabadi AH (2010) Approximate-analytical approach to nonlinear FDEs under generalized differentiability. J Adv Res Dyn Control Syst 2:56–74
    • (2010) J Adv Res Dyn Control Syst , vol.2 , pp. 56-74
    • Fard, O.S.1    Bidgoli, T.A.2    Borzabadi, A.H.3
  • 32
    • 34447518790 scopus 로고    scopus 로고
    • Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients
    • Fei W (2007) Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients. Inf Sci 177:329–4337
    • (2007) Inf Sci , vol.177 , pp. 329-4337
    • Fei, W.1
  • 33
    • 4243058286 scopus 로고    scopus 로고
    • Adaptative control of discrete-time chaotic system: a fuzzy control approach
    • Feng G, Chen G (2005) Adaptative control of discrete-time chaotic system: a fuzzy control approach. Chaos Solitons Fract 23:459–467
    • (2005) Chaos Solitons Fract , vol.23 , pp. 459-467
    • Feng, G.1    Chen, G.2
  • 35
    • 0042121384 scopus 로고    scopus 로고
    • Impulsive functional differential inclusions and fuzzy population models
    • Guo M, Xue X, Li R (2003) Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets Syst 138:601–615
    • (2003) Fuzzy Sets Syst , vol.138 , pp. 601-615
    • Guo, M.1    Xue, X.2    Li, R.3
  • 36
    • 0000443213 scopus 로고    scopus 로고
    • On solving the initial-value problems using the differential transformation method
    • Jang MJ, Chen CL, Liy YC (2000) On solving the initial-value problems using the differential transformation method. Appl Math Comput 115:145–160
    • (2000) Appl Math Comput , vol.115 , pp. 145-160
    • Jang, M.J.1    Chen, C.L.2    Liy, Y.C.3
  • 37
    • 12444324631 scopus 로고    scopus 로고
    • ∞ variable universe adaptive fuzzy control for chaotic systems
    • Jiang W, Guo-Dong Q, Bin D (2005) $$H_{\infty }$$H∞ variable universe adaptive fuzzy control for chaotic systems. Chaos Solitons Fract 24:1075–1086
    • (2005) Chaos Solitons Fract , vol.24 , pp. 1075-1086
    • Jiang, W.1    Guo-Dong, Q.2    Bin, D.3
  • 38
    • 33750331075 scopus 로고    scopus 로고
    • Simulating continuous fuzzy systems
    • Jowers LJ, Buckley JJ, Reilly KD (2007) Simulating continuous fuzzy systems. Inf Sci 177:436–448
    • (2007) Inf Sci , vol.177 , pp. 436-448
    • Jowers, L.J.1    Buckley, J.J.2    Reilly, K.D.3
  • 39
    • 0023573517 scopus 로고
    • Fuzzy differential equations
    • Kaleva O (1987) Fuzzy differential equations. Fuzzy Set Syst 24:301–317
    • (1987) Fuzzy Set Syst , vol.24 , pp. 301-317
    • Kaleva, O.1
  • 40
    • 0000363222 scopus 로고
    • The Cauchy problem for fuzzy differential equations
    • Kaleva O (1990) The Cauchy problem for fuzzy differential equations. Fuzzy Set Syst 35:389–396
    • (1990) Fuzzy Set Syst , vol.35 , pp. 389-396
    • Kaleva, O.1
  • 41
    • 30144435903 scopus 로고    scopus 로고
    • A note on fuzzy differential equations
    • Kaleva O (2006) A note on fuzzy differential equations. Nonlinear Anal 64:895–900
    • (2006) Nonlinear Anal , vol.64 , pp. 895-900
    • Kaleva, O.1
  • 43
    • 38349073450 scopus 로고    scopus 로고
    • Comparison results for fuzzy differential equations
    • Lopez RR (2008) Comparison results for fuzzy differential equations. Inf Sci 178:1756–1779
    • (2008) Inf Sci , vol.178 , pp. 1756-1779
    • Lopez, R.R.1
  • 44
    • 0000382276 scopus 로고    scopus 로고
    • Numerical solutions of fuzzy differential equations
    • Ma M, Friedman M, Kandel A (1999) Numerical solutions of fuzzy differential equations. Fuzzy Set Syst 105:133–138
    • (1999) Fuzzy Set Syst , vol.105 , pp. 133-138
    • Ma, M.1    Friedman, M.2    Kandel, A.3
  • 46
    • 49349119632 scopus 로고
    • A note on the extension principle for fuzzy sets
    • Nguyen HT (1978) A note on the extension principle for fuzzy sets. J Math Anal Appl 64:369–380
    • (1978) J Math Anal Appl , vol.64 , pp. 369-380
    • Nguyen, H.T.1
  • 47
  • 48
    • 34250789774 scopus 로고    scopus 로고
    • Existence uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument
    • Papaschinopoulos G, Stefanidou G, Efraimidi P (2007) Existence uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument. Inf Sci 177:3855–3870
    • (2007) Inf Sci , vol.177 , pp. 3855-3870
    • Papaschinopoulos, G.1    Stefanidou, G.2    Efraimidi, P.3
  • 49
    • 0001237908 scopus 로고
    • Differentials of fuzzy functions
    • Puri ML, Ralescu DA (1983) Differentials of fuzzy functions. J Math Anal Appl 91:552–558
    • (1983) J Math Anal Appl , vol.91 , pp. 552-558
    • Puri, M.L.1    Ralescu, D.A.2
  • 51
    • 0023581045 scopus 로고
    • On the fuzzy initial value problem
    • Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Set Syst 24:319–330
    • (1987) Fuzzy Set Syst , vol.24 , pp. 319-330
    • Seikkala, S.1
  • 52
    • 0009755102 scopus 로고    scopus 로고
    • Global existence of solutions to fuzzy differential equations
    • Song S, Guo L, Feng C (2000) Global existence of solutions to fuzzy differential equations. Fuzzy Set Syst 115:371–376
    • (2000) Fuzzy Set Syst , vol.115 , pp. 371-376
    • Song, S.1    Guo, L.2    Feng, C.3
  • 53
    • 79960565924 scopus 로고    scopus 로고
    • Numerical solutions for linear system of first-order fuzzy differential equations with fuzzy constant coefficients
    • Solaymani Fard O, Ghal-Eh N (2011) Numerical solutions for linear system of first-order fuzzy differential equations with fuzzy constant coefficients. Inf Sci 181:4765–4779
    • (2011) Inf Sci , vol.181 , pp. 4765-4779
    • Solaymani Fard, O.1    Ghal-Eh, N.2
  • 54
    • 34248666540 scopus 로고
    • Fuzzy sets. Inf
    • Zadeh LA (1965) Fuzzy sets. Inf. Control 8:338–353
    • (1965) Control , vol.8 , pp. 338-353
    • Zadeh, L.A.1


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