Random fuzzy functional integro-differential equations under generalized Hukuhara differentiability

In this paper, we prove the existence and uniqueness results for the random fuzzy functional integro-differential equations under generalized Hukuhara differentiability. For the existence and uniqueness, we use the method of successive approximations. Some kinds of boundedness of the solution are established. Moreover, we provide examples to illustrate the results.

[1]  W. Fei,et al.  Doob's Decomposition Theorem for Fuzzy (Super) Submartingales , 2004 .

[2]  M. T. Malinowski.  Random fuzzy differential equations under generalized Lipschitz condition , 2012 .

[3]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .

[4]  Tofigh Allahviranloo,et al.  Existence and Uniqueness of Solutions of Fuzzy Volterra Integro-differential Equations , 2010, IPMU.

[5]  W. Fei.  On the Theory of (Dual) Projection for Fuzzy Stochastic Processes , 2005 .

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

[7]  Tofigh Allahviranloo,et al.  A new method for solving fuzzy integro-differential equation under generalized differentiability , 2011, Neural Computing and Applications.

[8]  Weiyin Fei,et al.  Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients , 2007, Inf. Sci..

[9]  Jong Yeoul Park,et al.  On random fuzzy functional differential equations , 2013, Fuzzy Sets Syst..

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

[11]  V. Lakshmikantham,et al.  Fuzzy Differential Systems and the New Concept of Stability , 2001 .

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

[13]  J. Oguntuase.  ON AN INEQUALITY OF GRONWALL , 2000 .

[14]  Tofigh Allahviranloo,et al.  Fuzzy generalized H-differential and applications to fuzzy differential equations of second-order , 2014, J. Intell. Fuzzy Syst..

[15]  S. B. Boswell,et al.  A central limit theorem for fuzzy random variables , 1987 .

[16]  María Angeles Gil,et al.  Fuzzy random variables , 2001, Inf. Sci..

[17]  Ana Colubi,et al.  A _{}[0,1] representation of random upper semicontinuous functions , 2002 .

[18]  M. Puri,et al.  The Concept of Normality for Fuzzy Random Variables , 1985 .

[19]  J. Oguntuase.  ON INTEGRAL INEQUALITIES OF GRONWALL-BELLMAN-BIHARI TYPE IN SEVERAL VARIABLES , 2000 .

[20]  M. T. Malinowski.  Existence theorems for solutions to random fuzzy differential equations , 2010 .

[21]  M. Puri,et al.  Limit theorems for fuzzy random variables , 1986, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[22]  Marek T. Malinowski,et al.  Interval differential equations with a second type Hukuhara derivative , 2011, Appl. Math. Lett..

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

[24]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[25]  Tofigh Allahviranloo,et al.  Fuzzy fractional differential equations under generalized fuzzy Caputo derivative , 2014, J. Intell. Fuzzy Syst..

[26]  Weiyin Fei,et al.  Doob's stopping theorem for fuzzy (super, sub) martingales with discrete time , 2003, Fuzzy Sets Syst..

[27]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

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

[29]  Ngo Van Hoa,et al.  Fuzzy functional integro-differential equations under generalized H-differentiability , 2014, J. Intell. Fuzzy Syst..

[30]  Dan A. Ralescu,et al.  Tools for fuzzy random variables: Embeddings and measurabilities , 2006, Comput. Stat. Data Anal..

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

[32]  Y. Kuang.  Delay Differential Equations: With Applications in Population Dynamics , 2012 .

[33]  Weiyin Fei.  Regularity and stopping theorem for fuzzy martingales with continuous parameters , 2005, Inf. Sci..

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

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

[36]  Vasile Lupulescu,et al.  On a class of functional differential equations in Banach spaces , 2010 .

[37]  Marek T. Malinowski,et al.  On random fuzzy differential equations , 2009, Fuzzy Sets Syst..

[38]  Tofigh Allahviranloo,et al.  A New Method for Solving Fuzzy Volterra Integro-Differential Equations , 2011 .

[39]  T. Allahviranloo,et al.  Note on ''Generalized Hukuhara differentiability of interval-valued functions and interval differential equations'' , 2012 .