Research Article
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Year 2019, , 886 - 895, 31.12.2019
https://doi.org/10.17776/csj.632770

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

Year 2019, , 886 - 895, 31.12.2019
https://doi.org/10.17776/csj.632770

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.

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

Hülya Gültekin Çitil 0000-0002-3543-033X

Publication Date December 31, 2019
Submission Date October 14, 2019
Acceptance Date November 21, 2019
Published in Issue Year 2019

Cite

APA Gültekin Çitil, H. (2019). A Study on First-Order Fuzzy Initial Value Problems with Positive and Negative Fuzzy Number Coefficients by Fuzzy Laplace Transform. Cumhuriyet Science Journal, 40(4), 886-895. https://doi.org/10.17776/csj.632770