Document Type: Research Articles

**Author**

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

**Abstract**

The fuzzy linear second order equations with fuzzy initial values are investigated

in this paper. The analytic general solution solutions of them using

a rst solution is founded. The parametric form of fuzzy numbers is applied

to solve the second order equations. General solutions for fuzzy linear second

order equations with fuzzy initial values are investigated and formulated

in four cases. A example is solved to illustrate method better and solutions

are searched in four cases under Hakuhara derivation. Finally the solutions of

example are shown in gures for four cases.

in this paper. The analytic general solution solutions of them using

a rst solution is founded. The parametric form of fuzzy numbers is applied

to solve the second order equations. General solutions for fuzzy linear second

order equations with fuzzy initial values are investigated and formulated

in four cases. A example is solved to illustrate method better and solutions

are searched in four cases under Hakuhara derivation. Finally the solutions of

example are shown in gures for four cases.

**Keywords**

[1] T.Allahviranloo, N.Kiani, N.Barkhordari, Toward the existence and

uniqueness of solution of second order fuzzy dierential equations ,

Information sciences 179, 2009.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

2006.

[13]A. Kauman, M.M. Gupta, Introduction to Fuzzy Arithmetic: Theory and

Application, Van Nostrand Reinhold, New York, 1991.

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.

differential equations, Nonlinear analysis 72, 2010.

[15]V.Lupulescu, Initial value problem of fuzzy dierential equation under

dissipative condition , Information sciences 178, 2008.

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.

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.

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.

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.

Analysis and Applications 91, 1983.

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

1987.

1987.

[21]L. stefanini, B.Bede, Generalized Hukuhara dierentiability of intervalvalued

functions and interval differential equations , Nonlinear Analysis

71, 2009.

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

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.

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.

second order dierential equations under generalize H-dierentiability ,

Computers and mathematics with applications 60, 2010.

Volume 12, Issue 1

Winter and Spring 2018

Pages 77-91