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Published in: Soft Computing 3/2010

01-02-2010 | Original Paper

Fuzzy Laplace transforms

Authors: Tofigh Allahviranloo, M. Barkhordari Ahmadi

Published in: Soft Computing | Issue 3/2010

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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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Literature
go back to reference Abbasbandy S, Allahviranloo T (2002) Numerical solution of fuzzy differential equation by Tailor method. J Comput Method Appl Math 2:113–124MathSciNet Abbasbandy S, Allahviranloo T (2002) Numerical solution of fuzzy differential equation by Tailor method. J Comput Method Appl Math 2:113–124MathSciNet
go back to reference Abbasbandy S, Allahviranloo T, Lopez-Pouso O, Nieto JJ (2004) Numerical methods for fuzzy differential inclusions. Comput Math Appl 48(10–11):1633–1641MATHCrossRefMathSciNet Abbasbandy S, Allahviranloo T, Lopez-Pouso O, Nieto JJ (2004) Numerical methods for fuzzy differential inclusions. Comput Math Appl 48(10–11):1633–1641MATHCrossRefMathSciNet
go back to reference Allahviranloo T, Ahmady N, Ahmady E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Inform Sci 177/7:1633–1647MATHCrossRefMathSciNet Allahviranloo T, Ahmady N, Ahmady E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Inform Sci 177/7:1633–1647MATHCrossRefMathSciNet
go back to reference Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Set Syst 151:581–599MATHCrossRefMathSciNet Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Set Syst 151:581–599MATHCrossRefMathSciNet
go back to reference Bede B, Gal SG (2006) Remark on the new solutions of fuzzy differential equations. Chaos Solitons Fractals Bede B, Gal SG (2006) Remark on the new solutions of fuzzy differential equations. Chaos Solitons Fractals
go back to reference Bede B, Rudas IJ, Bencsik AL (2006) First order linear fuzzy differential equations under generalized differentiability. Inform Sci 177:1648–1662CrossRefMathSciNet Bede B, Rudas IJ, Bencsik AL (2006) First order linear fuzzy differential equations under generalized differentiability. Inform Sci 177:1648–1662CrossRefMathSciNet
go back to reference Buckley JJ (2006) Simulating continuous fuzzy systems. Springer Buckley JJ (2006) Simulating continuous fuzzy systems. Springer
go back to reference Chalco-Cano Y, Roman-Flores H (2006) On new solutions of fuzzy differential equations. Chaos Solitons Fractals 38:112–119CrossRefMathSciNet Chalco-Cano Y, Roman-Flores H (2006) On new solutions of fuzzy differential equations. Chaos Solitons Fractals 38:112–119CrossRefMathSciNet
go back to reference Congxin W, Shiji S (1998) Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditins. Inform Sci 108:123–134MATHCrossRefMathSciNet Congxin W, Shiji S (1998) Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditins. Inform Sci 108:123–134MATHCrossRefMathSciNet
go back to reference Dubios D, Prade H (1982) Towards fuzzy differential calculus. Fuzzy Set Syst 8:1–7, 105–116, 225–233 Dubios D, Prade H (1982) Towards fuzzy differential calculus. Fuzzy Set Syst 8:1–7, 105–116, 225–233
go back to reference Friedman M, Ming M, Kandel A (1999) Numerical solution of fuzzy differential and integral equations. Fuzzy Set Syst 106:35–48MATHCrossRef Friedman M, Ming M, Kandel A (1999) Numerical solution of fuzzy differential and integral equations. Fuzzy Set Syst 106:35–48MATHCrossRef
go back to reference 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 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
go back to reference Kandel A, Byatt WJ (1978) Fuzzy differential equations. In: Proceedings of the interational conference on cybernetics and society. Tokyo, pp 1213–12160 Kandel A, Byatt WJ (1978) Fuzzy differential equations. In: Proceedings of the interational conference on cybernetics and society. Tokyo, pp 1213–12160
go back to reference Menda W (1988) Linear fuzzy differential equation systems on R 1. J Fuzzy Syst Math 2(1):51–56 (in chinese) Menda W (1988) Linear fuzzy differential equation systems on R 1. J Fuzzy Syst Math 2(1):51–56 (in chinese)
go back to reference Song S, Wu C (2000) Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations. Fuzzy Set Syst 110:55–67MATHCrossRefMathSciNet Song S, Wu C (2000) Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations. Fuzzy Set Syst 110:55–67MATHCrossRefMathSciNet
go back to reference Wu HC (1999) The improper fuzzy Riemann integral and its numerical integration. Inform Sci 111:109–137CrossRef Wu HC (1999) The improper fuzzy Riemann integral and its numerical integration. Inform Sci 111:109–137CrossRef
go back to reference Wu HC (2000) The fuzzy Riemann integral and its numerical integration. Fuzzy Set Syst 110:1–25MATHCrossRef Wu HC (2000) The fuzzy Riemann integral and its numerical integration. Fuzzy Set Syst 110:1–25MATHCrossRef
go back to reference Xu J, Liao Z, Hu Z (2007) A class of linear differential dynamical systems with fuzzy initial condition. Fuzzy Set Syst 158:2339–2358MATHCrossRefMathSciNet Xu J, Liao Z, Hu Z (2007) A class of linear differential dynamical systems with fuzzy initial condition. Fuzzy Set Syst 158:2339–2358MATHCrossRefMathSciNet
go back to reference Zimmermann HJ (1991) Fuzzy set theory—and its applications. Kluwer Academic Publishers, Dordrecht Zimmermann HJ (1991) Fuzzy set theory—and its applications. Kluwer Academic Publishers, Dordrecht
Metadata
Title
Fuzzy Laplace transforms
Authors
Tofigh Allahviranloo
M. Barkhordari Ahmadi
Publication date
01-02-2010
Publisher
Springer-Verlag
Published in
Soft Computing / Issue 3/2010
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-008-0397-6

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