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Fuzzy Laplace transforms

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Abstract

In this paper we propose a fuzzy Laplace transform and under the strongly generalized differentiability concept, we use it in an analytic solution method for some fuzzy differential equations (FDEs). The related theorems and properties are proved in detail and the method is illustrated by solving some examples.

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References

  • Abbasbandy S, Allahviranloo T (2002) Numerical solution of fuzzy differential equation by Tailor method. J Comput Method Appl Math 2:113–124

    MathSciNet  Google Scholar 

  • Abbasbandy S, Allahviranloo T, Lopez-Pouso O, Nieto JJ (2004) Numerical methods for fuzzy differential inclusions. Comput Math Appl 48(10–11):1633–1641

    Article  MATH  MathSciNet  Google Scholar 

  • Allahviranloo T, Ahmady N, Ahmady E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Inform Sci 177/7:1633–1647

    Article  MATH  MathSciNet  Google Scholar 

  • Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Set Syst 151:581–599

    Article  MATH  MathSciNet  Google Scholar 

  • Bede B, Gal SG (2006) Remark on the new solutions of fuzzy differential equations. Chaos Solitons Fractals

  • Bede B, Rudas IJ, Bencsik AL (2006) First order linear fuzzy differential equations under generalized differentiability. Inform Sci 177:1648–1662

    Article  MathSciNet  Google Scholar 

  • Buckley JJ (2006) Simulating continuous fuzzy systems. Springer

  • Buckley JJ, Feuring T (1999) Introduction to fuzzy partial differential equations. Fuzzy Set Syst 105:241–248

    Article  MATH  MathSciNet  Google Scholar 

  • Buckley JJ, Feuring T (2003) Fuzzy differential equations. Fuzzy Sets Syst 110:43–54

    Article  MathSciNet  Google Scholar 

  • Chalco-Cano Y, Roman-Flores H (2006) On new solutions of fuzzy differential equations. Chaos Solitons Fractals 38:112–119

    Article  MathSciNet  Google Scholar 

  • Chang SSL, Zadeh L (1972) On fuzzy mapping and control. IEEE Trans Syst Cybern 2:30–34

    MATH  MathSciNet  Google Scholar 

  • Congxin W, Shiji S (1998) Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditins. Inform Sci 108:123–134

    Article  MATH  MathSciNet  Google Scholar 

  • Ding Z, Ma M, Kandel A (1997) Existence of the solutions of fuzzy differential equations with parameters. Inform Sci 99:205–217

    Article  MATH  MathSciNet  Google Scholar 

  • Dubios D, Prade H (1982) Towards fuzzy differential calculus. Fuzzy Set Syst 8:1–7, 105–116, 225–233

  • Friedman M, Ming M, Kandel A (1999) Numerical solution of fuzzy differential and integral equations. Fuzzy Set Syst 106:35–48

    Article  MATH  Google Scholar 

  • Goetschel R, Voxman W (1986) Elementery calculus. Fuzzy Set Syst 18:31–43

    Article  MATH  MathSciNet  Google Scholar 

  • He O, Yi W (1989) On fuzzy differential equations. Fuzzy Set Syst 32:321–325

    Article  MATH  Google Scholar 

  • Jowers LJ, Buckley JJ, Reilly KD (2007) Simulating continuous fuzzy systems. Inform Sci 177:436–448

    Article  MATH  MathSciNet  Google Scholar 

  • Kaleva O (1987) Fuzzy differential equations. Fuzzy Set Syst 24:301–317

    Article  MATH  MathSciNet  Google Scholar 

  • Kaleva O (1990) The Cauchy problem for fuzzy differential equations. Fuzzy Set Syst 35:389–396

    Article  MATH  MathSciNet  Google Scholar 

  • Kandel A (1980) Fuzzy dynamical systems and the nature of their solutions. In: Wang PP, Chang SK (eds) Fuzzy sets theory and application to policy analysis and information systems. Plenum Press, New York, pp 93–122

    Google Scholar 

  • Kandel A, Byatt WJ (1978) Fuzzy differential equations. In: Proceedings of the interational conference on cybernetics and society. Tokyo, pp 1213–12160

  • Kloeden P (1991) Remarks on Peano-like theorems for fuzzy differential equations. Fuzzy Set Syst 44:161–164

    Article  MATH  MathSciNet  Google Scholar 

  • Ma M, Friedman M, Kandel A (1999) Numerical solution of fuzzy differential equations. Fuzzy Set Syst 105:133–138

    Article  MATH  MathSciNet  Google Scholar 

  • Menda W (1988) Linear fuzzy differential equation systems on R 1. J Fuzzy Syst Math 2(1):51–56 (in chinese)

    Google Scholar 

  • Puri ML, Ralescu D (1983) Differential for fuzzy function. J Math Anal Appl 91:552–558

    Article  MATH  MathSciNet  Google Scholar 

  • Puri ML, Ralescu D (1986) Fuzzy random variables. J Math Anal Appl 114:409–422

    Article  MATH  MathSciNet  Google Scholar 

  • Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Set Syst 24:319–330

    Article  MATH  MathSciNet  Google Scholar 

  • Song S, Wu C (2000) Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations. Fuzzy Set Syst 110:55–67

    Article  MATH  MathSciNet  Google Scholar 

  • Wu HC (1999) The improper fuzzy Riemann integral and its numerical integration. Inform Sci 111:109–137

    Article  Google Scholar 

  • Wu HC (2000) The fuzzy Riemann integral and its numerical integration. Fuzzy Set Syst 110:1–25

    Article  MATH  Google Scholar 

  • Xu J, Liao Z, Hu Z (2007) A class of linear differential dynamical systems with fuzzy initial condition. Fuzzy Set Syst 158:2339–2358

    Article  MATH  MathSciNet  Google Scholar 

  • Zimmermann HJ (1991) Fuzzy set theory—and its applications. Kluwer Academic Publishers, Dordrecht

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, 14515/775, Tehran, Iran

    Tofigh Allahviranloo

  2. Science and Research Branch, Islamic Azad University (IAU), 14515/775, Tehran, Iran

    M. Barkhordari Ahmadi

Authors
  1. Tofigh Allahviranloo
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  2. M. Barkhordari Ahmadi
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Correspondence to Tofigh Allahviranloo.

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Allahviranloo, T., Ahmadi, M.B. Fuzzy Laplace transforms. Soft Comput 14, 235–243 (2010). https://doi.org/10.1007/s00500-008-0397-6

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  • DOI: https://doi.org/10.1007/s00500-008-0397-6

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