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Some solving methods for a fuzzy multi-point boundary value problem

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Abstract

In this paper, we consider a fuzzy multi-point boundary value problem-FMBVP [or a multi-point boundary value problem (MBVP) for fuzzy second-order differential equations (FSDEs) under generalized Hukuhara differentiability]. We present solving methods for a FMBVP in the space of fuzzy numbers \(E^{1}\), such that we have shown the ability to and methods to find solution of the MBVP for FSDEs in the form of \((FH^{gi}-FH^{gj})\)-solutions. In addition, we provide with a new idea to develop the real Green’s function method and give two examples being simple illustration of this FMBVP.

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References

  • Agarwal RP, Benchohra M, O’Regan D, Ouahab A (2005) Fuzzy solutions for multipoint boundary value problems. Mem Differ Equ Math Phys 35:1–14

    MATH  Google Scholar 

  • Bede B (2006) A note on ’Two-point boundary value problems associated with non-linear fuzzy differential equations’. Fuzzy Sets Syst 157:986–989

    Article  MathSciNet  Google Scholar 

  • 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  Google Scholar 

  • Chalco-Cano Y, Roman-Flore H (2008) On new solutions of fuzzy differential equations. Chaos Solitons Fractals 39:112–119

    Article  MathSciNet  Google Scholar 

  • Chalco-Cano Y, Rodrguez-Lpez R, Jimnez-Gamero MD (2016) Characterizations of generalized differentiable fuzzy functions. Fuzzy Sets Syst 295:37–56

    Article  MathSciNet  Google Scholar 

  • Chen M, Wu C, Xue X, Liu G (2008) On fuzzy boundary value problems. Inf Sci 178:1877–1892

    Article  MathSciNet  Google Scholar 

  • Gasilov NA, Amrahov SA, Fatullayev AG, Hashimoglu IF (2015) Solution method for a boundary problem with fuzzy forcing function. Inf Sci 317:340–368

    Article  MathSciNet  Google Scholar 

  • Hoa NV, Phu ND (2014) Fuzzy functional integro-differential equations under generalized H-differentiability. J Intell Fuzzy Syst 26:2073–2085

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Khastan A, Bahrami F, Ivaz K (2009) New results on multiple solutions for Nth-order fuzzy differential equations under generalized differentiability. Bound Value Probl 2009, Article ID 395714, p 13

  • Khastan A, Nieto JJ, Rodrguez-Lpez R (2013) Periodic boundary value problems for first-order linear differential equations with uncertainty under generalized differentiability. Inf Sci 222:544–558

    Article  MathSciNet  Google Scholar 

  • Lakshmikantham V, Murty KN, Turner J (2001) Two-point boundary problems associated with non-linear fuzzy differential equations. Math. Inequal Appl 4:527–533

    MathSciNet  MATH  Google Scholar 

  • O’Regan D, Lakshmikantham V, Nieto JJ (2002) Initial and boundary problems for fuzzy differential equations. Nonlinear Anal 54:405–415

    Article  MathSciNet  Google Scholar 

  • O’Regan D, Lakshmikantham V, Nieto J (2003) Initial and boundary value problems for fuzzy differential equations. Nonlinear Anal 54:405–415

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Dinh Phu

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Dinh Phu

  3. Faculty of Mathematics and Computer Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam

    Nguyen Nhut Hung

Authors
  1. Nguyen Dinh Phu
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  2. Nguyen Nhut Hung
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Correspondence to Nguyen Dinh Phu.

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Cite this article

Phu, N.D., Hung, N.N. Some solving methods for a fuzzy multi-point boundary value problem. Soft Comput 24, 483–499 (2020). https://doi.org/10.1007/s00500-019-03926-3

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  • DOI: https://doi.org/10.1007/s00500-019-03926-3

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