Exact Solution of Semi-linear Fuzzy System
Authors
-
Department of Applied Mathematics, Faculty of Technology and Engineering, The M. S. University of Baroda ,IN
Purnima K. Pandit
DOI:
https://doi.org/10.18311/jims/2017/15569Keywords:
Fuzzy Differential Equation, Fuzzy Initial Condition, Fuzzy NumberAbstract
In this paper we consider a semi-linear dynamical system with fuzzy initial condition. We discuss the results regarding the existence of the solution and obtain the best possible solution for such systems. We give a real life supportive illustration of population model, justify the need for fuzzy setup for the problem, and discuss the solution for it.
Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Purnima K. Pandit
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2017-02-23
Published 2017-07-01
References
Bede, Barnabs, and Sorin G. Gal., Generalizations of the dierentiability of fuzzy-number valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151, 3, (2005), 581-599.
Bede B., Note on Numerical solutions of fuzzy differential equations by predictor-corrector method, Information Sciences, 178, (2008), 1917-1922.
Buckley, James J., and Thomas Feuring. Fuzzy initial value problem for Nth-order linear differential equations, Fuzzy Sets and Systems, 121, 2, (2001), 247-255.
Chang, Sheldon SL, and Lofti A. Zadeh. On fuzzy mapping and control, IEEE Transactions on Systems, Man and Cybernetics, SMC-2, 1, (1972), 30-34.
Diamond, Phil. Brief note on the variation of constants formula for fuzzy differential equations, Fuzzy Sets and Systems, 129, 1, (2002), 65-71.
Dubois, Didier, and Henri Prade. Towards fuzzy differential calculus part 3: Differentiation, Fuzzy sets and systems, 8, 3, (1982), 225-233.
Gasilov N.A., Fatullayev A.G., Amrahov S. E., Khastan A. A new approach to fuzzy initial value problem, Soft Computing, 18, 2, (2014), 217-225.
Georgiou, D. N., Juan J. Nieto, and Rosana Rodriguez-Lopez. Initial value problems for higher-order fuzzy differential equations, Nonlinear Analysis: Theory, Methods and Applications, 63, 4, (2005), 587-600.
Goetschel G., Voxman W., Elementary fuzzy calculus, Fuzzy Sets and Systems, 18, (1986), 31-43.
Gopal, M. Modern Control System Theory, New Age International, 1993
Kaleva, O. Fuzzy differential equations, Fuzzy Sets and Systems, 24, (1987), 301-317.
Kaleva, O. The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35, (1990), 389-396.
Lakshmikantham, V. and Mohapatra, R. Basic properties of solutions of fuzzy differential equations, Nonlinear Studies, 8, (2001), 113-124.
Ma, Ming, Menahem Friedman, and Abraham Kandel. Numerical solutions of fuzzy differential equations, Fuzzy sets and systems, 105, 1, (1999), 133-138.
Puri, Madan L., and Dan A. Ralescu. Fuzzy random variables, Journal of mathematical analysis and applications, 114, 2, (1986), 409-422.
Nieto, Juan J. The Cauchy problem for continuous fuzzy differential equations, Fuzzy Sets and Systems, 102, 2 (1999), 259-262.
Park, Jong Yeoul, and Hyo Keun Han. Fuzzy differential equations, Fuzzy Sets and Systems, 110, 1, (2000), 69-77.
Seikkala, Seppo. On the fuzzy initial value problem Fuzzy sets and systems, 24, 3, (1987), 319-330.
Tapaswini Smita and Chakraverty S., New Centre Based Approach for the Solution of nth Order Interval Differential Equation, Reliable Computing, 20, (2014), 25-44.
Lofti A. Zadeh, Fuzzy sets, Information and Control, 8, (1965), 338-353.
Kreyszig, Erwin. Introductory functional analysis with applications, John Wiley and Sons, 1989.
Wu HC, The improper fuzzy Riemann integral and its numerical integration, Inform Sci, 111, (1999), 109-137.
7