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Mathematics 2019, 7(3), 231; https://doi.org/10.3390/math7030231

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

1
Mathematics Department, Khwaja Fareed University of Engineering and Information Technology, Rahimyar khan-64200, Pakistan
2
Department of computer Science, Islamia University Bahawalpur, Bahawalpur 63100, Pakistan
*
Author to whom correspondence should be addressed.
Current address: Department of Computer Science and Information Technology, The Islamia University, Bahawalpur, Bahawalpur 63100, Pakistan.
These authors contributed equally to this work.
Received: 31 January 2019 / Revised: 24 February 2019 / Accepted: 25 February 2019 / Published: 1 March 2019
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
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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. View Full-Text
Keywords: fuzzy differential transformation; min, max operators; fuzzy Taylor series; fuzzy initial value problems fuzzy differential transformation; min, max operators; fuzzy Taylor series; fuzzy initial value problems
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Salamat, N.; Mustahsan, M.; Saad Missen, M.M. Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method. Mathematics 2019, 7, 231.

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