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

Document Type: Research Articles


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


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.


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

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

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

[4]B. Bede, I.J. Rudas, A.L. Bencsik, First order linear fuzzy di erential
equations under genaralizes di erentiability , Information Sciences 177,

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

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

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

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

[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 di erential
equations by fuzzy laplace transfom method, Advances in Di erence
Equations , 2015.

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

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

[13]A. Kau man, 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 di erential equation under
dissipative condition , Information sciences 178, 2008.

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

[17]N. Parandin, Numerical solutions of fuzzy second order di erential
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 di erential equations with fuzzy initial condition ,
International Journal of Science and research Vol 3, 428-431, 2014.

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

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

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

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

[23]L. Wang, S. Guo, Adomian method for second order Fuzzy di erential
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 di erential equations under generalize H-di erentiability ,
Computers and mathematics with applications 60, 2010.