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A new method for solving fuzzy linear differential equations

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Abstract

In this paper, a novel operator method is proposed for solving fuzzy linear differential equations under the assumption of strongly generalized differentiability. To this end, the equivalent integral form of the original problem is obtained then by using its lower and upper functions the solutions in the parametric forms are determined. The proposed method is illustrated with numerical examples.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Allahviranloo T, Barkhordari Ahmadi M (2010) Fuzzy Laplace transforms. Soft Comput 14: 235–243

    Article  MATH  Google Scholar 

  4. Allahviranloo T, Kiani NA, Barkhordari M (2009) Toward the existence and uniqueness of solutions of second-order fuzzy differental equations. Inf Sci 179: 1207–1215

    Article  MathSciNet  MATH  Google Scholar 

  5. Allahviranloo T, Kiani NA, Motamedi N (2009) Solving fuzzy differential equations by differential transformation method. Inf Sci 179: 956–966

    Article  MathSciNet  MATH  Google Scholar 

  6. Allahviranloo T, Salahshour S (2010) Euler method for solving hybrid fuzzy differential equation. Soft Comput. doi:10.1007/s00500-010-0659-y

  7. Agarwal RP, Lakshmikantham V, Nieto JJ (2010) On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal 72: 2859–2862

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. Diamond P, Kloeden P (1994) Metric spaces of fuzzy sets. World Scientific, Singapore

    MATH  Google Scholar 

  12. Georgiou DN, Nieto JJ, Rodriguez R (2005) Initial value problems for higher-order fuzzy differential equations. Nonlinear Anal 63: 587–600

    Article  MathSciNet  MATH  Google Scholar 

  13. Khastan A, Bahrami F, Ivaz K (2010) New results on multiple solutions for Nth-order fuzzy differential equation under generalized differentiability. Boundary Value Problem (Hindawi Publishing Corporation). doi:10.1155/2009/395714

  14. Khastan A, Nieto JJ (2010) A boundary value problem for second order fuzzy differential equations. Nonlinear Anal 72: 3583–3593

    Article  MathSciNet  MATH  Google Scholar 

  15. Nieto JJ, Rodriguez-Lopez R (2006) Hybrid metric dynamical systems with impulses. Nonlinear Anal 64: 368–380

    Article  MathSciNet  MATH  Google Scholar 

  16. Nieto JJ, Rodriguez-Lopez R, Franco D (2006) Linear first-order fuzzy differential equations. Int J Uncertain Fuzziness Knowledge-Based Syst 14: 687–709

    Article  MathSciNet  MATH  Google Scholar 

  17. Nieto JJ, Rodriguez-Lopez R, Georgiou DN (2008) Fuzzy differential systems under generalized metric spaces approach. Dyn Syst Appl 17: 1–24

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  22. Xu J, Liao Z, Nieto JJ (2010) A class of linear differential dynamical systems with fuzzy matrices. J Math Anal Appl 368: 54–68

    Article  MathSciNet  MATH  Google Scholar 

  23. Zimmermann HJ (1991) Fuzzy set theory and its applications. Kluwer, Dordrecht

    MATH  Google Scholar 

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Authors and Affiliations

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

    T. Allahviranloo & S. Abbasbandy

  2. Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran

    S. Salahshour & A. Hakimzadeh

Authors
  1. T. Allahviranloo
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  2. S. Abbasbandy
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  3. S. Salahshour
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  4. A. Hakimzadeh
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Corresponding authors

Correspondence to T. Allahviranloo or S. Salahshour.

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Allahviranloo, T., Abbasbandy, S., Salahshour, S. et al. A new method for solving fuzzy linear differential equations. Computing 92, 181–197 (2011). https://doi.org/10.1007/s00607-010-0136-6

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  • DOI: https://doi.org/10.1007/s00607-010-0136-6

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