Authors

1 Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

2 Department of Mathematics, Tehran Science and Research Branch, Islamic Azad University, Tehran , Iran

Abstract

In this paper, we study first order linear fuzzy differential equations with fuzzy coefficient and initial value. We use the generalized differentiability concept and apply the exponent matrix to present the general form of their solutions. Finally, one example is given to illustrate our results.

Keywords

Main Subjects

[1] T. Allahviranloo, A method for solving nth order fuzzy linear differential equations, International Journal of Computer Mathematics 89 (4) (2009), pp. 730-742.
 
[2] B. Bede, I.J. Rudas, and A.L. Bencsik, First order linear fuzzy di erential equations under generalized differentiability, Information Science 177 (2007), pp. 1648-1662.
 
[3] B. Bede and S.G. Gal, Generalizations of the differentiability of fuzzy number value functions with applications to fuzzy differential equations, Fuzzy Sets and Systems 151 (2005), pp. 581-599.
 
[4] B. Bede and S.G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Sets and Systems 147 (2004), pp. 385-403.
 
[5] Y. Chalco-Cano and H. Romn-Flores, On new solutions of fuzzy differential equations, Chaos, Solitons and Fractals 38 (2008) , pp.112-119.
 
[6] P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets, World Scienti c, Singapore, 1994.
 
[7] D. Dubois and H. Prade, Towards fuzzy differential calculus: Part 3, di erentiation, Fuzzy Sets and Systems 8 (1982), pp. 225-233.
 
[8] R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986), pp. 31-43.
 
[9] S. G. Gal, Approximation theory in fuzzy setting, in: G.A. Anastassiou (Ed.), Handbook of Analytic-Computational Methods in Applied Mathematics, Chapman Hall CRC Press, 2000, pp. 617-666.
 
[10] O. He and W. Yi, On fuzzy differential equations, Fuzzy Sets and Systems 24 (1989), pp. 321-325.
 
[11] O.Kaleva, fuzzy differential equations, Fuzzy Sets and Systems 24 (1987), pp. 301-317.
 
[12] O.Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems 35(1990), pp. 389-396.
 
[13] A. Khastan, J.J. Nieto and R. R. Lopez, Variation of constant formula for rst order fuzzy differential equations, Fuzzy Sets and Systems.
 
[14] A. Khastan, F. Bahrami and K. Ivaz, New results on multiple solutions for Nth-order fuzzy differential equations under generalized differentiability, Boundary Value Problems (2009) 13p, Article ID 395714.
 
[15] P.Kloeden, Remark on peano-like theorems for fuzzy differential equations, Fuzzy Sets and Systems 44 (1991),pp. 161-164.
 
[16] W. Menda, Linear fuzzy differential equation system on, Journal of Fuzzy Systems Mathematics 2 (1) (1988), pp. 51-56,in Chinese.
 
[17] M. Puri, D. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications 91 (1983) 552-558.
 
[18] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987), pp. 319-330.
 
[19] C. Wu and Z. Gong, On Henstock integral of fuzzy-number-valued functions I, Fuzzy Sets and Systems, 120 (2001), pp. 523-532.
 
[20] L. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Information Sciences 172 (2005), pp. 1-40.