International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Semi Analytical Solution for Fuzzy Autonomous Differential Equations

  • Mazin H. Suhhiem*
  • Raad I. Khwayyit

    * Corresponding author

    Abstract

    In this work, we have used fuzzy Adomian decomposition method to find the fuzzy semi analytical solution of the fuzzy autonomous differential equations with fuzzy initial conditions. This method allows for the solution of the fuzzy initial value problems to be calculated in the form of an infinite fuzzy series in which the fuzzy components can be easily calculated. The fuzzy series solutions that we have obtained are accurate solutions and very close to the fuzzy exact analytical solutions. Some numerical results have been given to illustrate the efficiency of the used method.

    How to Cite

    M. H. Suhhiem, R. I. Khwayyit, Semi Analytical Solution for Fuzzy Autonomous Differential Equations, Int. J. Anal. Appl. 20 (2022), 61. https://doi.org/10.28924/2291-8639-20-2022-61

    BibTeX
    @article{Suhhiem2022,
      author  = {Suhhiem, Mazin H. and Khwayyit, Raad I.},
      title   = {Semi Analytical Solution for Fuzzy Autonomous Differential Equations},
      journal = {Int. J. Anal. Appl.},
      volume  = {20},
      year    = {2022},
      pages   = {61},
      doi     = {10.28924/2291-8639-20-2022-61}
    }

    References

    • [1] T. Allahviranloo, L. Jamshidi, Solution of Fuzzy Differential Equations Under Generalized Differentiability by Adomian Decomposition Method, Iran. J. Optim. 1 (2009), 57-75.
    • [2] L. Wang, S. Guo, Adomian Method for Second-Order Fuzzy Differential Equation, Int. J. Math. Comput. Sci. 5 (2011), 613-616.
    • [3] S. Narayanamoorthy, T. Yookesh, An Adomian Decomposition Method to Solve Linear Fuzzy Differential Equations, in: Proceeding of the International Conference on Mathematical Methods and Computation, India, 13-14 February 2014.
    • [4] M. Paripour, E. Hajilou, A. Hajilou, H. Heidari, Application of Adomian Decomposition Method to Solve Hybrid Fuzzy Differential Equations, J. Taibah Univ. Sci. 9 (2015), 95–103. https://doi.org/10.1016/j.jtusci.2014.06.002.
    • [5] A. Jameel, Numerical and Approximate – Analytical Solutions of Fuzzy Initial Value Problems, Ph.D. Thesis, School of Quantitative Sciences, University Utara Malaysia, Malaysia, 2015.
    • [6] S. Biswas, S. Banerjee, T. Roy, Solving Intuitionistic Fuzzy Differential Equations with Linear Differential Operator by Adomian Decomposition Method, Notes IFS, 22 (2016), 25-41. http://ifigenia.org/wiki/issue:nifs/22/4/25-41.
    • [7] S. Biswas, T. Roy, Adomian Decomposition Method for Fuzzy Differential Equations with Linear Differential Operator, J. Inform. Comput. Sci. 11 4 (2016), 243-250.
    • [8] M. Suhhiem, Fuzzy Artificial Neural Network for Solving Fuzzy and Non-Fuzzy Differential Equations, Ph.D. Thesis, College of Sciences, University of Al-Mustansiriyah, Iraq, 2016.
    • [9] A.K. Ateeah, Approximate Solution for Fuzzy Differential Algebraic Equations of Fractional Order Using Adomian Decomposition Method, Ibn Al-Haitham J. Pure Appl. Sci. 30 (2017), 202-213.
    • [10] S. Askari, T. Allahviranloo, S. Abbasbandy, Solving Fuzzy Fractional Differential Equations by Adomian Decomposition Method Used in Optimal Control Theory, Int. Trans. J. Eng. Manage. Appl. Sci. Technol. 10 (2019), 10A12P.
    • [11] H.A. Sabr, B.N. Abood, M. Suhhiem, Fuzzy Homotopy Analysis Method for Solving Fuzzy Autonomous Differential Equation, Ratio Math. 40 (2021), 191-212. https://doi.org/10.23755/rm.v40i1.589.