Research Article
Year 2020,
Volume: 10 Issue: 1, 576 - 583, 01.03.2020
Abstract
This study is on solutions of a fuzzy problem with variable coefficient. Solutions are found by fuzzy Laplace transform. Generalized differentiability is used. It is searched whether the solutions are valid 𝛼-level sets or not. Examples are solved on studied problem. Conclusions are given.
Keywords
Fuzzy initial value problem fuzzy Laplace transform generalized differentiability triangular fuzzy number
References
- Ahmad N, Mamat M, Kavikumar J, Amir Hamzah NS, 2012. Solving fuzzy duffing’s equation by the fuzzy Laplace transform decomposition. Applied Mathematical Sciences, 6(59):2935-2944.
- Allahviranloo T, Barkhordari Ahmadi M, 2010. Fuzzy Laplace transforms, Soft Computing, 14(3):235-243.
- Bede B, 2008. Note on ‘‘Numerical solutions of fuzzy differential equations by predictor-corrector method’’. Information Sciences, 178(7):1917-1922.
- Bede B, Rudas IJ, Bencsik AL, 2007. First order linear fuzzy differential equations under generalized differentiability. Information Sciences, 177(7):1648-1662.
- Buckley JJ, Feuring T, Hayashi Y, 2002. Linear systems of first order ordinary differential equations: Fuzzy initial conditions. Soft Computing, 6(6):415-421.
- Ceylan T, Altınışık N, 2018. Fuzzy eigenvalue problem with eigenvalue parameter contained in the boundary condition. Journal of Science and Arts, 3(44):589-602.
- Fatullayev AG, Can E, Köroğlu C, 2013. Numerical solution of a boundary value problem for a second order fuzzy differential equation, TWMS Journal of Pure and Applied Mathematics, 4(2):169-176.
- Gültekin H, Altınışık N, 2014. On solution of two-point fuzzy boundary value problems. The Bulletin of Society for Mathematical Services and Standards, 11:31-39.
- Gültekin Çitil H, 2018. 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):781-787.
- Hüllermeier E, 1997. An approach to modelling and simulation of uncertain dynamical systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5(2):117-137.
- Khastan A, Bahrami F, Ivaz K, 2009. New results on multiple solutions for nth-order fuzzy differential equations under generalized differentiability. Boundary Value Problems, doi:10.1155/2009/395714, 1-13.
- Khastan A, Nieto JJ, 2010. A boundary value problem for second order fuzzy differential equations. Nonlinear Analysis, 72(9-10):3583-3593.
- Liu H-K, 2011. Comparison results of two-point fuzzy boundary value problems. International Journal of Computational and Mathematical Sciences, 5(1):1-7.
- Mondal SP, Banerjee S, Roy TK, 2013. First order linear homogeneous ordinary differential equation in fuzzy environment. International Journal of Pure and Applied Sciences and Technology, 14(1):16-26.
- Mondal SP, Roy TK, 2015. Generalized intuitionistic fuzzy Laplace transform and its application in electrical circuit. TWMS Journal of Applied and Engineering Mathematics, 5(1):30-45.
- Patel KR, Desai NB, 2017. Solution of variable coefficient fuzzy differential equations by fuzzy Laplace transform. International Journal on Recent and Innovation Trends in Computing and Communication, 5(6):927-942.
- Puri ML, Ralescu DA, 1983. Differentials of fuzzy functions. Journal of Mathematical Analysis and Applications, 91(2):552-558.
- Ramazannia Tolouti SJ, Barkhordary Ahmadi M, 2010. Fuzzy Laplace transform on two order derivative and solving fuzzy two order differential equations. International Journal of Industrial Mathematics, 4(2):279-293.
- Salahshour S. Allahviranloo T, 2013. Applications of fuzzy Laplace transforms. Soft Computing, 17(1):145-158.
- Stefanini L, Bede B, 2008. Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Analysis, 71(3-4):1311-1328.
- Zadeh LA, 1965. Fuzzy sets. Information and Control, 8(3):338-353.
- Zadeh LA, 1975. The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, 8(3):199-249.
Year 2020,
Volume: 10 Issue: 1, 576 - 583, 01.03.2020
Abstract
This study is on solutions of a fuzzy problem with variable coefficient. Solutions are found by fuzzy Laplace transform. Generalized differentiability is used. It is searched whether the solutions are valid 𝛼-level sets or not. Examples are solved on studied problem. Conclusions are given.
Keywords
Fuzzy initial value problem fuzzy Laplace transform generalized differentiability triangular fuzzy number
References
- Ahmad N, Mamat M, Kavikumar J, Amir Hamzah NS, 2012. Solving fuzzy duffing’s equation by the fuzzy Laplace transform decomposition. Applied Mathematical Sciences, 6(59):2935-2944.
- Allahviranloo T, Barkhordari Ahmadi M, 2010. Fuzzy Laplace transforms, Soft Computing, 14(3):235-243.
- Bede B, 2008. Note on ‘‘Numerical solutions of fuzzy differential equations by predictor-corrector method’’. Information Sciences, 178(7):1917-1922.
- Bede B, Rudas IJ, Bencsik AL, 2007. First order linear fuzzy differential equations under generalized differentiability. Information Sciences, 177(7):1648-1662.
- Buckley JJ, Feuring T, Hayashi Y, 2002. Linear systems of first order ordinary differential equations: Fuzzy initial conditions. Soft Computing, 6(6):415-421.
- Ceylan T, Altınışık N, 2018. Fuzzy eigenvalue problem with eigenvalue parameter contained in the boundary condition. Journal of Science and Arts, 3(44):589-602.
- Fatullayev AG, Can E, Köroğlu C, 2013. Numerical solution of a boundary value problem for a second order fuzzy differential equation, TWMS Journal of Pure and Applied Mathematics, 4(2):169-176.
- Gültekin H, Altınışık N, 2014. On solution of two-point fuzzy boundary value problems. The Bulletin of Society for Mathematical Services and Standards, 11:31-39.
- Gültekin Çitil H, 2018. 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):781-787.
- Hüllermeier E, 1997. An approach to modelling and simulation of uncertain dynamical systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5(2):117-137.
- Khastan A, Bahrami F, Ivaz K, 2009. New results on multiple solutions for nth-order fuzzy differential equations under generalized differentiability. Boundary Value Problems, doi:10.1155/2009/395714, 1-13.
- Khastan A, Nieto JJ, 2010. A boundary value problem for second order fuzzy differential equations. Nonlinear Analysis, 72(9-10):3583-3593.
- Liu H-K, 2011. Comparison results of two-point fuzzy boundary value problems. International Journal of Computational and Mathematical Sciences, 5(1):1-7.
- Mondal SP, Banerjee S, Roy TK, 2013. First order linear homogeneous ordinary differential equation in fuzzy environment. International Journal of Pure and Applied Sciences and Technology, 14(1):16-26.
- Mondal SP, Roy TK, 2015. Generalized intuitionistic fuzzy Laplace transform and its application in electrical circuit. TWMS Journal of Applied and Engineering Mathematics, 5(1):30-45.
- Patel KR, Desai NB, 2017. Solution of variable coefficient fuzzy differential equations by fuzzy Laplace transform. International Journal on Recent and Innovation Trends in Computing and Communication, 5(6):927-942.
- Puri ML, Ralescu DA, 1983. Differentials of fuzzy functions. Journal of Mathematical Analysis and Applications, 91(2):552-558.
- Ramazannia Tolouti SJ, Barkhordary Ahmadi M, 2010. Fuzzy Laplace transform on two order derivative and solving fuzzy two order differential equations. International Journal of Industrial Mathematics, 4(2):279-293.
- Salahshour S. Allahviranloo T, 2013. Applications of fuzzy Laplace transforms. Soft Computing, 17(1):145-158.
- Stefanini L, Bede B, 2008. Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Analysis, 71(3-4):1311-1328.
- Zadeh LA, 1965. Fuzzy sets. Information and Control, 8(3):338-353.
- Zadeh LA, 1975. The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, 8(3):199-249.
There are 22 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Matematik / Mathematics |
| Authors | |
| Publication Date | March 1, 2020 |
| Submission Date | July 31, 2019 |
| Acceptance Date | November 4, 2019 |
| Published in Issue | Year 2020 Volume: 10 Issue: 1 |
