Fuzzy Laplace transform method for the Ulam stability of linear fuzzy differential equations of first order with constant coefficients

In the present paper, the notion of fuzzy multiplication-convolution is introduced. Meantime, an important property is derived, which is similar to the Laplace transform of an ordinary convolution. By using the fuzzy Laplace transform and the preceding property, this paper deals with the Ulam stability of three variants of first order linear fuzzy differential equations with constant coefficients.

[1]  Takeshi Miura,et al.  ON THE HYERS-ULAM STABILITY OF A DIFFERENTIABLE MAP , 2002 .

[2]  Barnabás Bede,et al.  Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations , 2005, Fuzzy Sets Syst..

[3]  Y Chalco Cano,et al.  ON NEW SOLUTIONS OF FUZZY DIFFERENTIAL EQUATIONS , 2008 .

[4]  Juan J. Nieto,et al.  Variation of constant formula for first order fuzzy differential equations , 2011, Fuzzy Sets Syst..

[5]  Faxing Wang,et al.  A fixed point approach to the Ulam stability of fuzzy differential equations under generalized differentiability , 2016, J. Intell. Fuzzy Syst..

[6]  Soon-Mo Jung,et al.  Hyers-Ulam stability of linear differential equations of first order, II , 2006, Appl. Math. Lett..

[7]  Takeshi Miura,et al.  ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy , 2002 .

[8]  Imre J. Rudas,et al.  First order linear fuzzy differential equations under generalized differentiability , 2007, Inf. Sci..

[9]  Claudi Alsina,et al.  On Some Inequalities and Stability Results Related to the Exponential Function , 1998 .

[10]  Takeshi Miura,et al.  On the Hyers-Ulam Stability of Real Continuous Function Valued Differentiable Map , 2001 .

[11]  Yonghong Shen Hyers-Ulam-Rassias stability of first order linear partial fuzzy differential equations under generalized differentiability , 2015 .

[12]  Laécio C. Barros,et al.  Fuzzy differential equations: An approach via fuzzification of the derivative operator , 2013, Fuzzy Sets Syst..

[13]  Li Sun,et al.  Hyers-Ulam stability of linear differential equations of first order , 2008, Appl. Math. Lett..

[14]  Soon-Mo Jung,et al.  Legendre's Differential Equation and Its Hyers-Ulam Stability , 2007 .

[15]  Osmo Kaleva Fuzzy differential equations , 1987 .

[16]  Tofigh Allahviranloo,et al.  Applications of fuzzy Laplace transforms , 2013, Soft Comput..

[17]  Barnabás Bede,et al.  Generalized differentiability of fuzzy-valued functions , 2013, Fuzzy Sets Syst..

[18]  Tofigh Allahviranloo,et al.  Fuzzy Laplace transforms , 2009, Soft Comput..

[19]  Yonghong Shen,et al.  On the Ulam stability of first order linear fuzzy differential equations under generalized differentiability , 2015, Fuzzy Sets Syst..

[20]  Nasser Mikaeilvand,et al.  Laplace transform formula on fuzzy nth-order derivative and its application in fuzzy ordinary differential equations , 2014, Soft Comput..

[21]  J P Aubin FUZZY DIFFERENTIAL INCLUSIONS , 1990 .

[22]  George A. Anastassiou A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE , 2010 .

[23]  Soon-Mo Jung,et al.  Laplace transform and Hyers–Ulam stability of linear differential equations , 2013 .