Normalized expression for solutions to linear fuzzy differential equations under combination of differences

We give a normalized expression for the solutions to the initial value problem for some linear fuzzyinterval dierential equations by using a general notation which allows the combination of two types of dierences. By switching between these types of differences, we derive several expressions for solutions corresponding to strongly generalized dierentiability, providing a general formulation for these solutions to linear problems.

[1]  Barnabás Bede,et al.  Solutions of fuzzy differential equations based on generalized differentiability , 2010 .

[2]  Luciano Stefanini,et al.  A generalization of Hukuhara difference and division for interval and fuzzy arithmetic , 2010, Fuzzy Sets Syst..

[3]  J. Wasowski,et al.  Differential Equations with Fuzzy Parameters via Differential Inclusions , 2001 .

[4]  Eyke Hüllermeier,et al.  Numerical Methods for Fuzzy Initial Value Problems , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[6]  Phil Diamond,et al.  Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations , 1999, IEEE Trans. Fuzzy Syst..

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

[8]  S. Seikkala.  On the fuzzy initial value problem , 1987 .

[9]  J. Nieto,et al.  FUZZY DIFFERENTIAL SYSTEMS UNDER GENERALIZED METRIC SPACES APPROACH , 2008 .

[10]  Y. Chalco-Cano,et al.  Comparation between some approaches to solve fuzzy differential equations , 2009, Fuzzy Sets Syst..

[11]  Yurilev Chalco-Cano,et al.  Calculus for interval-valued functions using generalized Hukuhara derivative and applications , 2013, Fuzzy Sets Syst..

[12]  W. A. Lodwick,et al.  Fuzzy differential equations and Zadeh's extension principle , 2011, 2011 Annual Meeting of the North American Fuzzy Information Processing Society.

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

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

[15]  Rosana Rodríguez-López.  On the existence of solutions to periodic boundary value problems for fuzzy linear differential equations , 2013, Fuzzy Sets Syst..

[16]  Osmo Kaleva.  The Cauchy problem for fuzzy differential equations , 1990 .

[17]  Heriberto Román-Flores,et al.  A note on Zadeh's extensions , 2001, Fuzzy Sets Syst..

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

[19]  Yurilev Chalco-Cano,et al.  Fuzzy differential equations and the extension principle , 2007, Inf. Sci..

[20]  Juan J. Nieto,et al.  Fuzzy delay differential equations under generalized differentiability , 2014, Inf. Sci..

[21]  V. Lakshmikantham,et al.  PERSPECTIVES OF FUZZY INITIAL VALUE PROBLEMS , 2007 .

[22]  D. Dubois,et al.  Towards fuzzy differential calculus part 3: Differentiation , 1982 .

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

[24]  Osmo Kaleva.  Fuzzy differential equations , 1987 .

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

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

[27]  Luciano Stefanini,et al.  Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations , 2012 .

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

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

[30]  Phil Diamond,et al.  Stability and periodicity in fuzzy differential equations , 2000, IEEE Trans. Fuzzy Syst..

[31]  P. Kloeden,et al.  Metric Spaces Of Fuzzy Sets Theory And Applications , 1975 .

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

[33]  Juan J. Nieto,et al.  NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS UNDER GENERALIZED DIFFERENTIABILITY , 2009 .

[34]  Juan J. Nieto,et al.  Linear First-Order Fuzzy Differential Equations , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[35]  Vasile Lupulescu,et al.  On a class of fuzzy functional differential equations , 2009, Fuzzy Sets Syst..

[36]  Yurilev Chalco-Cano,et al.  Some remarks on fuzzy differential equations via differential inclusions , 2013, Fuzzy Sets Syst..

[37]  Luciano Stefanini,et al.  Parametric representation of fuzzy numbers and application to fuzzy calculus , 2006, Fuzzy Sets Syst..

[38]  V. Lakshmikantham,et al.  Fuzzy Differential Inclusions , 2003 .