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Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method

Author

Listed:
  • Nadeem Salamat

    (Mathematics Department, Khwaja Fareed University of Engineering and Information Technology, Rahimyar khan-64200, Pakistan
    Current address: Department of Computer Science and Information Technology, The Islamia University, Bahawalpur, Bahawalpur 63100, Pakistan.
    These authors contributed equally to this work.)

  • Muhammad Mustahsan

    (Mathematics Department, Khwaja Fareed University of Engineering and Information Technology, Rahimyar khan-64200, Pakistan
    These authors contributed equally to this work.)

  • Malik M. Saad Missen

    (Department of computer Science, Islamia University Bahawalpur, Bahawalpur 63100, Pakistan)

Abstract

The first-order fuzzy differential equation has two possible solutions depending on the definition of differentiability. The definition of differentiability changes as the product of the function and its first derivative changes its sign. This switching of the derivative’s definition is handled with the application of min, max operators. In this paper, a numerical technique for solving fuzzy initial value problems is extended to solving higher-order fuzzy differential equations. Fuzzy Taylor series is used to develop the fuzzy differential transformation method for solving this problem. This leads to a single solution for higher-order differential equations.

Suggested Citation

  • Nadeem Salamat & Muhammad Mustahsan & Malik M. Saad Missen, 2019. "Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method," Mathematics, MDPI, vol. 7(3), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:231-:d:210223
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    References listed on IDEAS

    as
    1. Barnab?s Bede & Luciano Stefanini, 2012. "Generalized Differentiability of Fuzzy-valued Functions," Working Papers 1209, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    2. Faranak Rabiei & Fudziah Ismail & Ali Ahmadian & Soheil Salahshour, 2013. "Numerical Solution of Second-Order Fuzzy Differential Equation Using Improved Runge-Kutta Nystrom Method," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-10, May.
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