General Solution for Fuzzy Linear Second Order Differential Equation Using First Solution

Subject Areas : Applied Mathematics

Laleh Hooshangian ¹

1 - Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran.

Received: 2018-03-14 Accepted : 2018-03-14 Published : 2018-05-01

Keywords: Fuzzy initial values, General solution, Linear differential equation, First solution,

Abstract :

The fuzzy linear second order equations with fuzzy initial values are investigatedin this paper. The analytic general solution solutions of them usinga rst solution is founded. The parametric form of fuzzy numbers is appliedto solve the second order equations. General solutions for fuzzy linear secondorder equations with fuzzy initial values are investigated and formulatedin four cases. A example is solved to illustrate method better and solutionsare searched in four cases under Hakuhara derivation. Finally the solutions ofexample are shown in gures for four cases.

References:

[1] T.Allahviranloo, N.Kiani, N.Barkhordari, Toward the existence and
uniqueness of solution of second order fuzzy dierential equations ,
Information sciences 179, 2009.

[2]Allahviranloo. T, Hooshangian. L, Fuzzy Generalized H-Dierential and
Applications to Fuzzy Dierential Equations of Second-Order, Intelligent
and Fuzzy Systems, 26 (2014) 1951-1967.

[3]B.Bede, S.G.Gal, Generalizations of dierentiability of fuzzy number value
function with applications to fuzzy dierential equations , Fuzzy sets and
systems151, 2005.

[4]B. Bede, I.J. Rudas, A.L. Bencsik, First order linear fuzzy dierential
equations under genaralizes dierentiability , Information Sciences 177,
2007.

[5]J. Buckley, T. Feuring, M.D. Jimenez-Gamero, Fuzzy dierential equation,
Fuzzy Sets and Systems 110, 2000.

[6]Y. Chalco-Cano, H. Roman-Flores, Fuzzy dierential equations with
generalized derivative , 27th ANFIPS International Conference IEEE,
2008.

[7]Y. Chalco-Cano, H. Roman-Flores, On new solutions of fuzzy dierntial
equations , Chaos solitons and fractals 38, 2008.
89

[8]Y. Chalco-Cano, H. Roman-Flores, M.D. Jimenez-Gamero, Generalized
derivative and derivative for set-valued functions , Information Science,
2011.

[9]P. Diamond, Brief note on the variation of constance formula for fuzzy
differential equations ,fuzzy sets and systems 129 , 2002.

[10]E. Eljaoui, S. Mellani, L. S. Chadli, Solving second order fuzzy dierential
equations by fuzzy laplace transfom method, Advances in Dierence
Equations , 2015.

[11]O. Kaleva, Fuzzy dierential equations,fuzzy sets and systems 24, 1987.

[12]O. Kaleva, A note on fuzzy differential equations , Nonlinear Analysis 64,
2006.

[13]A. Kauman, M.M. Gupta, Introduction to Fuzzy Arithmetic: Theory and
Application, Van Nostrand Reinhold, New York, 1991.

[14]A. Khastan, J.J.Nieto, Aboundary value problem for second order fuzzy
differential equations, Nonlinear analysis 72, 2010.

[15]V.Lupulescu, Initial value problem of fuzzy dierential equation under
dissipative condition , Information sciences 178, 2008.

[16]J.J. Nieto, R.R. Lopez, Fuzzy dierential system under generalized metric
space approach , Dynamic System Application 17, 2008.

[17]N. Parandin, Numerical solutions of fuzzy second order dierential
equations of 2nd-order by Runge-Kutta method , Journal of mathematical
extension Vol 7. No 3, 47-62, 2013.

[18]V. Parimala, P. Rajarajeswari, V. Nirvala, A second order Runge-Kutta
method to solve Fuzzy dierential equations with fuzzy initial condition ,
International Journal of Science and research Vol 3, 428-431, 2014.

[19]M. Puri, D. Ralescu, Dierential and fuzzy functions , Mathematics
Analysis and Applications 91, 1983.

[20]S. Siekalla, On the fuzzy initial value problem , Fuzzy sets and systems,
1987.

[21]L. stefanini, B.Bede, Generalized Hukuhara dierentiability of intervalvalued
functions and interval differential equations , Nonlinear Analysis
71, 2009.

[22]L. Stefanini, A generalization of Hukuhara dierence and division for
interval and fuzzy arithmetics, Fuzzy sets and systems 161, 2010.
90

[23]L. Wang, S. Guo, Adomian method for second order Fuzzy dierential
equation, International Journal of mathematical, computational physical,
electrical and computer engineering, Vol 5, 613-616, 2011.

[24]L.A. Zadeh, Fuzzy Sets, Information and Control 8, 1965.

[25]D. Zhang, W.Feng, Y.Zhao, J.Qiu, Global existence of solutions for fuzzy
second order dierential equations under generalize H-dierentiability ,
Computers and mathematics with applications 60, 2010.