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The Residual Power Series Method for Solving the Fractional Fuzzy Delay Differential Equation

  • Qiujuan TongEmail author
  • Yongzhen ZangEmail author
  • Jianke ZhangEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)

Abstract

In this paper, the fuzzy delay differential equation is expressed in fractional form, and the Residual Power Series Method (RPSM) is used to solve the equation. The delay differential equation indicates that in a system, the speed of the system is not only related to the current state of the system, but also depends on the historical trajectory until this moment. Due to the existence of systematic errors, fractional fuzzy delay differential equations play an important role in more and more system models in biology, engineering, physics and other sciences. Maple was used to calculate the numerical solution of this equation, and the results are presented in the form of a graph. The results show that it is an effective method when solving the fractional fuzzy delay differential equation. By this method, the approximate solutions of the fractional fuzzy delay differential equation can be obtained with just a few steps.

Keywords

Residual Power Series Method Fractional fuzzy delay differential equation Caputo derivative 

References

  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  2. 2.
    Jafari, R.: Solving fuzzy differential equation with bernstein neural networks. In: 2016 IEEE International Conference on Systems, Man, and Cybernetics \(\bullet \) SMC 2016, pp. 001245-001250. IEEE, Budapest (2016)Google Scholar
  3. 3.
    Allahviranloo, T., Salahshour, S.: Euler method for solving hybrid fuzzy differential equation. Soft Comput. - Fusion Found. Methodologies Appl. 15(7), 1247–1253 (2011)zbMATHGoogle Scholar
  4. 4.
    Ahmad, L., Farooq, M., Abdullah, S.: Solving n-th order fuzzy differential equation by fuzzy Laplace transform. Indian J. Pure Appl. Math. (2014) Google Scholar
  5. 5.
    Tapaswini, S., Chakraverty, S.: Numerical solution of n-th order fuzzy linear differential equations by homotopy perturbation method. Int. J. Comput. Appl. 64(6), 5–10 (2013)zbMATHGoogle Scholar
  6. 6.
    Tehran, I.: Numerical solutions of fuzzy differential equations by taylor method. Comput. Methods Appl. Math. 2(2), 113–124 (2002)MathSciNetGoogle Scholar
  7. 7.
    Abu, A.O.: Series solution of fuzzy equations under strongly generalized differentiability. J. Adv. Res. Appl. Math. 5, 31–52 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Tchier, F., Inc, M., Korpinar, Z.S.: Solutions of the time fractional reaction-diffusion equations with residual power series method. Adv. Mech. Eng. 8(10), 1–10 (2016)CrossRefGoogle Scholar
  9. 9.
    Alquran, M.: Analytical solutions of fractional foam drainage equation by residual power series method. Math. Sci. 8(4), 153–160 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Dubois, D.: Towards fuzzy differential calculus part 3: differentiation. Fuzzy Sets Syst. 8(3), 225–233 (1982)CrossRefGoogle Scholar
  11. 11.
    Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18(1), 31–43 (1986)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Seikkala, S.: On the fuzzy initial value problem. Fuzzy Sets Syst. 24(3), 319–330 (1987)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Wu, C., Gong, Z.: On Henstock integral of fuzzy-number-valued functions. Fuzzy Sets Syst. 120(120), 523–532 (2001)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Podlubny, I.: Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. In: Mathematics in Science and Engineering , vol. 198, pp. 1–340 (1999)Google Scholar
  15. 15.
    El-Ajou, A., Abu Arqub, O., Al, Z.Z.: New results on fractional power series: theories and applications. Entropy 15, 5305–5323 (2013)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Hamood, M.Y., Ali, F.J.: New analytical method for solving fuzzy delay differential equations. In: AIP Conference Proceedings, vol. 1691, pp. 040028-1–040028-8. AIP Publishing, Malaysia (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Xi’an University of Posts and TelecommunicationsXi’anChina

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