Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles

Abstract We study the existence and uniqueness of solution for fuzzy initial value problems in the setting of a generalized Hukuhara derivative and by using some recent results of fixed point of weakly contractive mappings on partially ordered sets.

[1]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[2]  J. Harjani,et al.  Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations , 2010 .

[3]  Binayak S. Choudhury,et al.  A Generalisation of Contraction Principle in Metric Spaces , 2008 .

[4]  Siegfried Gottwald,et al.  Applications of fuzzy sets to systems analysis , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

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

[6]  Juan J. Nieto,et al.  Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations , 2007 .

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

[8]  Osmo Kaleva Fuzzy differential equations , 1987 .

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

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

[11]  Yurilev Chalco-Cano,et al.  A note on generalized convexity for fuzzy mappings through a linear ordering , 2013, Fuzzy Sets Syst..

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

[13]  A. Ran,et al.  A fixed point theorem in partially ordered sets and some applications to matrix equations , 2003 .

[14]  M. Hukuhara INTEGRATION DES APPLICAITONS MESURABLES DONT LA VALEUR EST UN COMPACT CONVEXE , 1967 .

[15]  Rosana Rodríguez-López,et al.  Periodic boundary value problems for first-order linear differential equations with uncertainty under generalized differentiability , 2013, Inf. Sci..

[16]  B. Rhoades,et al.  Some theorems on weakly contractive maps , 2001 .

[17]  Luciano Stefanini,et al.  A Generalization of Hukuhara Difference , 2008, SMPS.

[18]  Y Chalco Cano,et al.  GENERALIZED DERIVATIVE AND -DERIVATIVE FOR SET-VALUED FUNCTIONS , 2011 .

[19]  Marek T. Malinowski,et al.  Interval Cauchy problem with a second type Hukuhara derivative , 2012, Inf. Sci..

[20]  Ravi P. Agarwal,et al.  Generalized contractions in partially ordered metric spaces , 2008 .

[21]  Juan J. Nieto,et al.  Applications of Contractive-like Mapping Principles to Fuzzy Equations , 2006 .

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

[23]  H Roman Flores,et al.  EMBEDDING OF LEVEL-CONTINUOUS FUZZY SETS ON BANACH SPACES , 2002 .

[24]  Rosana Rodríguez-López,et al.  Existence of extremal solutions for quadratic fuzzy equations , 2005 .

[25]  H. Banks,et al.  A Differential Calculus for Multifunctions , 1970 .

[26]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[27]  Juan J. Nieto,et al.  Fixed point theorems in ordered abstract spaces , 2007 .

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

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

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

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

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

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

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

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

[36]  Donal O'Regan,et al.  Fixed point theorems for generalized contractions in ordered metric spaces , 2008 .

[37]  M. Puri,et al.  DIFFERENTIAL FOR FUZZY FUNCTION , 1983 .

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

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

[40]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[41]  Barnabás Bede,et al.  Mathematics of Fuzzy Sets and Fuzzy Logic , 2012, Studies in Fuzziness and Soft Computing.