Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations

Abstract In this paper, we introduce new solutions for fuzzy differential equations as mixed solutions, and prove the existence and uniqueness of global solutions for fuzzy initial value problems involving integro-differential operators of Volterra type. One example is also given by applying mixed solution concept to fuzzy linear differential equations for obtaining their global solutions.

[1]  Vasile Lupulescu,et al.  On the fractional differential equations with uncertainty , 2011 .

[2]  A. Khastan,et al.  New Results on Multiple Solutions for th-Order Fuzzy Differential Equations under Generalized Differentiability , 2009 .

[3]  Jiuping Xu,et al.  A class of linear differential dynamical systems with fuzzy matrices , 2010 .

[4]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[5]  M. Puri,et al.  Differentials of fuzzy functions , 1983 .

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

[7]  Dimitris N. Georgiou,et al.  Initial value problems for higher-order fuzzy differential equations , 2005 .

[8]  Eyke Hüllermeier,et al.  An Approach to Modelling and Simulation of Uncertain Dynamical Systems , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9]  V. Lakshmikantham,et al.  Initial and boundary value problems for fuzzy differential equations , 2003 .

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

[11]  Congxin Wu,et al.  On Henstock integral of fuzzy-number-valued functions (I) , 2001, Fuzzy Sets Syst..

[12]  A. D. R. Choudary,et al.  On Peano theorem for fuzzy differential equations , 2011, Fuzzy Sets Syst..

[13]  Juan J. Nieto,et al.  The Cauchy problem for continuous fuzzy differential equations , 1999, Fuzzy Sets Syst..

[14]  Ravi P. Agarwal,et al.  Viability theory and fuzzy differential equations , 2005, Fuzzy Sets Syst..

[15]  Ravi P. Agarwal,et al.  A stacking theorem approach for fuzzy differential equations , 2003 .

[16]  Sorin G. Gal Approximation Theory in Fuzzy Setting , 2000 .

[17]  J. Nieto,et al.  A boundary value problem for second order fuzzy differential equations , 2010 .

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