Fuzzy differential equations with generalized derivative

In this paper we study fuzzy differential equations with generalized derivative. We obtain some properties of the generalized derivative. We discuss the equivalence of the fuzzy Cauchy problem and an Aumann-type integral equation. This study also makes some observations on the existence of solutions.

[1]  Maysam F. Abbod,et al.  Survey of utilisation of fuzzy technology in Medicine and Healthcare , 2001, Fuzzy Sets Syst..

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

[3]  H. Román-Flores,et al.  On new solutions of fuzzy differential equations , 2008 .

[4]  X. Liao,et al.  Fuzzy modeling and synchronization of hyperchaotic systems , 2005 .

[5]  Yurilev Chalco-Cano,et al.  Robinson’s chaos in set-valued discrete systems☆ , 2005 .

[6]  D. P. Datta,et al.  The golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology , 2003, 1001.1688.

[7]  Yurilev Chalco-Cano,et al.  Some chaotic properties of Zadeh’s extensions☆ , 2008 .

[8]  Zuohua Ding,et al.  Existence of the Solutions of Fuzzy Differential Equations with Parameters , 1997, Inf. Sci..

[9]  Xiaoping Xue,et al.  On the structure of solutions for fuzzy initial value problem , 2006, Fuzzy Sets Syst..

[10]  Xiaoping Xue,et al.  Impulsive functional differential inclusions and fuzzy population models , 2003, Fuzzy Sets Syst..

[11]  E.Stanley Lee,et al.  Approximate Solutions, Existence, and Uniqueness of the Cauchy Problem of Fuzzy Differential Equations☆ , 1996 .

[12]  Shiji Song,et al.  Global existence of solutions to fuzzy differential equations , 2000, Fuzzy Sets Syst..

[13]  Phil Diamond,et al.  Brief note on the variation of constants formula for fuzzy differential equations , 2002, Fuzzy Sets Syst..

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

[15]  Azriel Rosenfeld,et al.  Geodesic Visibility in Graphs , 1998, Inf. Sci..

[16]  M. S. El Naschie,et al.  From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold , 2005 .

[17]  Heriberto Román-Flores,et al.  Embedding of level-continuous fuzzy sets on Banach spaces , 2002, Inf. Sci..

[18]  V. Lakshmikantham,et al.  Theory of Fuzzy Differential Equations and Inclusions , 2003 .

[19]  Saeid Abbasbandy,et al.  Tuning of reachable set in one dimensional fuzzy differential inclusions , 2005 .

[20]  Michael Oberguggenberger,et al.  Differential Equations With Fuzzy Parameters , 1999 .

[21]  B. Bede,et al.  Fuzzy Differential Equations in Modeling of Hydraulic Differential Servo Cylinders , 2006 .

[22]  Osmo Kaleva,et al.  A note on fuzzy differential equations , 2006 .

[23]  Shiji Song,et al.  Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations , 2000, Fuzzy Sets Syst..

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

[25]  V. Lakshmikantham,et al.  Revisiting fuzzy differential equations , 2004 .

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

[27]  Michael Hanss,et al.  Applied Fuzzy Arithmetic: An Introduction with Engineering Applications , 2004 .

[28]  Xiaoping Xue,et al.  The oscillation of delay differential inclusions and fuzzy biodynamics models , 2003 .

[29]  Michelle LaBrunda,et al.  Fuzzy Logic in Medicine , 2008, J. Inf. Technol. Res..

[30]  J. Nieto,et al.  Bounded solutions for fuzzy differential and integral equations , 2006 .

[31]  Jong Yeoul Park,et al.  Fuzzy differential equations , 2000, Fuzzy Sets Syst..

[32]  H. R. Flores,et al.  SOBRE ECUACIONES DIFERENCIALES DIFUSAS , 2008 .

[33]  Congxin Wu,et al.  Existence Theorem to the Cauchy Problem of Fuzzy Differential Equations under Compactness-Type Conditions , 1998, Inf. Sci..