Skip to main content
SpringerLink
Log in

Some Existence Results for Fuzzy Differential Equations with a Metric-Basic Derivative of Type (ii)

  • Conference paper
  • First Online:
Fuzzy Logic and Technology, and Aggregation Operators (EUSFLAT 2023, AGOP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14069))

  • 380 Accesses

Abstract

In this paper, we investigate sufficient conditions for the existence of a solution for a dynamical system based on a metric structure \((G,u_N)\). Moreover, a slight variation in the assumptions allows to apply it for fuzzy functions. So, we study the existence of the solution to fuzzy differential equations under the concept of metric differentiability.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bede, B.: Mathematics of Fuzzy Sets and Fuzzy Logic. Springer, Berlin (2013). https://doi.org/10.1007/978-3-642-35221-8

    Book  MATH  Google Scholar 

  2. Buckley, J.J., Feuring, T.: Fuzzy differential equations. Fuzzy Sets Syst. 110, 43–54 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chalco-Cano, Y., Román-Flores, H.: Comparation between some approaches to solve fuzzy differential equations. Fuzzy Sets Syst. 160, 1517–1527 (2009)

    Article  MATH  Google Scholar 

  4. Chalco-Cano, Y., Rodríguez-López, R., Jiménez-Gamero, M.D.: Characterizations of generalized differentiable fuzzy functions. Fuzzy Sets Syst. 295, 37–56 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Diamond, P., Kloeden, P.: Metric Spaces of Fuzzy Sets. World Scientific, Singapore (1994)

    MATH  Google Scholar 

  6. Hüllermeier, E.: An approach to modelling and simulation of uncertain dynamical systems. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 5, 117–137 (1997)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Khastan, A., Rodríguez-López, R., Shahidi, M.: New metric-based derivatives for fuzzy functions and properties. Fuzzy Sets Syst. 436, 32–54 (2021)

    Article  MathSciNet  Google Scholar 

  9. Lakshmikantham, V., Nieto, J.J.: Differential equations in metric spaces: an introduction and an application to fuzzy differential equations. Dyn. Continuous Discrete Impulsive Syst. 10, 991–1000 (2003)

    MathSciNet  MATH  Google Scholar 

  10. Lupulescu, V., O’Regan, D.: A new derivative concept for set-valued and fuzzy-valued functions. Differential and integral calculus in quasilinear metric spaces. Fuzzy Sets Syst. 404, 75–110 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nieto, J.J., Rodríguez-López, R.: Euler polygonal method for metric dynamical systems. Inf. Sci. 177, 4256–4270 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Panasyuk, A.I.: Quasidifferential equations in metric spaces. Differ. Equ. 21, 914–921 (1985)

    MathSciNet  MATH  Google Scholar 

  13. Pederson, S., Sambandham, M.: Numerical solution to hybrid fuzzy systems. Math. Comput. Model. 45, 1133–1144 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This article was partially supported by Fapesp under grants no. 2022/00196-1 and 2020/09838-0 and by CNPq under grant no. 313313/2020-2.

Author information

Authors and Affiliations

  1. Department of Mathematics, Statistic and Scientific Computing, Unicamp, Campinas, Brazil

    Mina Shahidi & Estevão Esmi

  2. CITMAga, Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas; Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Rosana Rodríguez-López

Authors
  1. Mina Shahidi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rosana Rodríguez-López
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Estevão Esmi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mina Shahidi .

Editor information

Editors and Affiliations

  1. University of the Balearic Islands, Palma, Spain

    Sebastia Massanet

  2. University of Oviedo, Gijón, Spain

    Susana Montes

  3. University of the Balearic Islands, Palma, Spain

    Daniel Ruiz-Aguilera

  4. University of the Balearic Islands, Palma, Spain

    Manuel González-Hidalgo

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Shahidi, M., Rodríguez-López, R., Esmi, E. (2023). Some Existence Results for Fuzzy Differential Equations with a Metric-Basic Derivative of Type (ii). In: Massanet, S., Montes, S., Ruiz-Aguilera, D., González-Hidalgo, M. (eds) Fuzzy Logic and Technology, and Aggregation Operators. EUSFLAT AGOP 2023 2023. Lecture Notes in Computer Science, vol 14069. Springer, Cham. https://doi.org/10.1007/978-3-031-39965-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-39965-7_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-39964-0

  • Online ISBN: 978-3-031-39965-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation