Research Article
Year 2019,
Volume: 40 Issue: 4, 886 - 895, 31.12.2019
Abstract
References
- [1] Kadel A. and Byatt W.J., Fuzzy Differential Equations, in: Proceedings of International Conference Cybernetics and Society, Tokyo, (1978) 1213-1216.
- [2] Zadeh L.A., The Concept of a Linguistic Variable and its Application to Approximate Reasoning, Information Sciences, 8 (1975) 199-251.
- [3] Hüllermeier E., An Approach to Modelling and Simulation of Uncertain Dynamical Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5-2 (1997) 117-137.
- [4] Kaleva O., Fuzzy Differential Equations, Fuzzy Sets and Systems, 24-3 (1987) 301-317. [5] Gültekin H. and Altınışık N., On Solution of Two-Point Fuzzy Boundary Value Problems, The Bulletin of Society for Mathematical Services and Standards, 11 (2014) 31-39.
- [6] Bede B., Rudas I.J. and Bencsik A.L., First Order Linear Fuzzy Differential Equations under Generalized Differentiability, Information Sciences, 177-7 (2007) 1648-1662. [7] Gültekin Çitil H., The Relationship between the Solutions according to the Noniterative Method and the Generalized Differentiability of the Fuzzy Boundary Value Problem, Malaya Journal of Matematik, 6-4 (2018) 781-787.
- [8] Ceylan T. and Altınışık N., Fuzzy Eigenvalue Problem with Eigenvalue Parameter Contained in the Boundary Condition, Journal of Science and Arts, 3-44 (2018) 589-602.
- [9] Allahviranloo T. and Barkhordari Ahmadi M., Fuzzy Laplace Transforms, Soft Computing, 14-3 (2010) 235-243.
- [10] Patel K.R. and Desai N.B., Solution of Fuzzy Initial Value Problems by Fuzzy Laplace Transform, Kalpa Publications in Computing, 2 (2017) 25-37. [11] Patel K.R. and Desai N.B., Solution of Variable Coefficient Fuzzy Differential Equations by Fuzzy Laplace Transform, International Journal on Recent and Innovation Trends in Computing and Communication, 5-6 (2017) 927-942.
- [12] Liu H.-K., Comparison Results of Two-Point Fuzzy Boundary Value Problems, International Journal of Computational and Mathematical Sciences, 5-1 (2011) 1-7. [13] Salahshour S. and Allahviranloo T., Applications of Fuzzy Laplace Transforms, Soft Computing, 17-1 (2013) 145-158.
- [14] Shirin S. and Saha G.K., A New Computational Methodology to Find Appropriate Solutions of Fuzzy Equations, Mathematical Theory and Modeling, 2-1 (2011) 1-10.
- [15] Lakshmikantham V. and Mohapatra R.N., Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis, London, New York, 2003.
- [16] Khastan A. and Nieto J.J., A Boundary Value Problem for Second Order Fuzzy Differential Equations, Nonlinear Analysis: Theory, Methods and Applications, 72-9-10 (2010) 3583-3593.
A Study on First-Order Fuzzy Initial Value Problems with Positive and Negative Fuzzy Number Coefficients by Fuzzy Laplace Transform
Abstract
In this paper, fuzzy initial value problems for first-order fuzzy
differential equations with positive and negative fuzzy number coefficients are
studied by fuzzy Laplace transform. Solutions are found under the approach of
generalized differentiability. Examples are solved. Figures of the solutions
are drawn using the Mathematica program. Finally, conclusions are given.
Keywords
Fuzzy Initial Value Problem Generalized Differentiability Fuzzy Laplace Transform Positive and Negative Fuzzy Numbers
References
- [1] Kadel A. and Byatt W.J., Fuzzy Differential Equations, in: Proceedings of International Conference Cybernetics and Society, Tokyo, (1978) 1213-1216.
- [2] Zadeh L.A., The Concept of a Linguistic Variable and its Application to Approximate Reasoning, Information Sciences, 8 (1975) 199-251.
- [3] Hüllermeier E., An Approach to Modelling and Simulation of Uncertain Dynamical Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5-2 (1997) 117-137.
- [4] Kaleva O., Fuzzy Differential Equations, Fuzzy Sets and Systems, 24-3 (1987) 301-317. [5] Gültekin H. and Altınışık N., On Solution of Two-Point Fuzzy Boundary Value Problems, The Bulletin of Society for Mathematical Services and Standards, 11 (2014) 31-39.
- [6] Bede B., Rudas I.J. and Bencsik A.L., First Order Linear Fuzzy Differential Equations under Generalized Differentiability, Information Sciences, 177-7 (2007) 1648-1662. [7] Gültekin Çitil H., The Relationship between the Solutions according to the Noniterative Method and the Generalized Differentiability of the Fuzzy Boundary Value Problem, Malaya Journal of Matematik, 6-4 (2018) 781-787.
- [8] Ceylan T. and Altınışık N., Fuzzy Eigenvalue Problem with Eigenvalue Parameter Contained in the Boundary Condition, Journal of Science and Arts, 3-44 (2018) 589-602.
- [9] Allahviranloo T. and Barkhordari Ahmadi M., Fuzzy Laplace Transforms, Soft Computing, 14-3 (2010) 235-243.
- [10] Patel K.R. and Desai N.B., Solution of Fuzzy Initial Value Problems by Fuzzy Laplace Transform, Kalpa Publications in Computing, 2 (2017) 25-37. [11] Patel K.R. and Desai N.B., Solution of Variable Coefficient Fuzzy Differential Equations by Fuzzy Laplace Transform, International Journal on Recent and Innovation Trends in Computing and Communication, 5-6 (2017) 927-942.
- [12] Liu H.-K., Comparison Results of Two-Point Fuzzy Boundary Value Problems, International Journal of Computational and Mathematical Sciences, 5-1 (2011) 1-7. [13] Salahshour S. and Allahviranloo T., Applications of Fuzzy Laplace Transforms, Soft Computing, 17-1 (2013) 145-158.
- [14] Shirin S. and Saha G.K., A New Computational Methodology to Find Appropriate Solutions of Fuzzy Equations, Mathematical Theory and Modeling, 2-1 (2011) 1-10.
- [15] Lakshmikantham V. and Mohapatra R.N., Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis, London, New York, 2003.
- [16] Khastan A. and Nieto J.J., A Boundary Value Problem for Second Order Fuzzy Differential Equations, Nonlinear Analysis: Theory, Methods and Applications, 72-9-10 (2010) 3583-3593.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | December 31, 2019 |
| Submission Date | October 14, 2019 |
| Acceptance Date | November 21, 2019 |
| Published in Issue | Year 2019Volume: 40 Issue: 4 |