On Solution of First Order Initial Value Problems Using Laplace Transform In Fuzzy Environment
This study aimed at solving a nonhomogeneous linear first order initial value problem by means of Laplace transform method in fuzzy environment. The conditions for a fuzzy function to be
H−differentiable and gH−differentiability are well established. Finally, example is constructed to test the applicability or otherwise of the established results.
L. A. Zadeh, Fuzzy sets, Information and Control, 8(1965), 338-353.
Dubois, D and H.Parade 1978, Operation on Fuzzy Number. International Journal of Fuzzy system, 9:613-626.
A. Kandel and W. J. Byatt, “Fuzzy differential equations,” in Proceedings of the International Conference on Cybernetics and Society, pp. 1213–1216, Tokyo, Japan, 1978.
A. Kandel and W. J. Byatt, “Fuzzy processes,” Fuzzy Sets and Systems, vol. 4, no. 2, pp. 117–152, 1980.
A. Bencsik, B. Bede, J. Tar, J. Fodor, Fuzzy differential equations in modeling hydraulic differential servo cylinders, in: Third Romanian_Hungarian Joint Symposium on Applied Computational Intelligence, SACI, Timisoara, Romania, 2006.
J. J. Buckley and T. Feuring, “Fuzzy differential equations,” Fuzzy Sets and Systems, vol. 110, no. 1, pp.43–54, 2000.
B. Bede, I.J. Rudas, A.L. Bencsik, First order linear fuzzy differential equations under generalized differentiability, Information Sciences 177 (2007) 1648–1662.
James J. Buckley, Thomas Feuring, Fuzzy initial value problem for Nth-order linear differential equations, Fuzzy Sets and Systems 121 (2001) 247–255.
J.J. Buckley, T. Feuring, Y. Hayashi, Linear System of first order ordinary differential equations: fuzzy initial condition, soft computing 6 (2002) 415-421.
L.J. Jowers, J.J. Buckley, K.D. Reilly, Simulating continuous fuzzy systems, Information Sciences 177 (2007) 436–448.
S. R. Mondal, T. K. Roy, first order linear non homogeneous ordinary differential equation in fuzzy environment. Journal of Mathematica Theory and Modelling, 3 (1), (2013).
Hassan Zarei, Ali Vahidian Kamyad, and Ali Akbar Heydari, Fuzzy Modeling and Control of HIV Infection, Computational and Mathematical Methods in Medicine Volume 2012, Article ID 893474, 17 pages.
G.L. Diniz, J.F.R. Fernandes, J.F.C.A. Meyer, L.C. Barros, A fuzzy Cauchy problem modeling the decay of the biochemical oxygen demand in water, 2001 IEEE.
L.C. Barros, R.C. Bassanezi, P.A. Tonelli, Fuzzy modelling in population dynamics, Ecol. Model. 128 (2000) 27-33.
M. Oberguggenberger, S. Pittschmann, Differential equations with fuzzy parameters, Math. Modelling Syst. 5 (1999) 181-202.
S. R. Mondal, T. K. Roy, first order linear homogeneous ordinary differential equation in fuzzy environment based on laplace transform. Journal of mathematics computer science. 3 (2013) 1533-1564.
S. R. Mondal, T. K. Roy, first order linear non homogeneous ordinary differential equation in fuzzy nvironment based on laplace transform. Journal fuzzy set valued analysis. (2013) 1-18.
S. R. Mondal, T. K. Roy, first order linear homogeneous ordinary differential equation in fuzzy environment based on lagranges multiplier method. Journal of Uncertainty in Mathematical Science, 3 vol. 2014 (2014) 1-17.
S. R. Mondal, T. K. Roy, first order linear homogeneous ordinary differential equation in fuzzy environment. International Journal of Pure and Applied Sciences and Technology, 14(1) (2013) 16-26.
S. R. Mondal, T. K. Roy, solution of second order linear ordinary differential equation in fuzzy environment. Journal of Fuzzy Mathematics and Informatics, 3 (2015) 1-31.
S. R. Mondal, T. K. Roy, system of differential equation with initial value as triangular intuitionistic fuzzy number and its application. International Journal of Computer Mathematics, 3 (2015) 449-474.
This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.