Fuzzy generalized H-differential and applications to fuzzy differential equations of second-order

In this paper, a new way of obtaining second order Hakuhara derivative is introduced. The theorems to apply this way are approved. Then, the parametric form of fuzzy numbers is applied to solve two types of fuzzy H-differential equations of second order with constant multipliers and fuzzy initial values. Their solutions are classified and discussed hereinafter.

[1]  James J. Buckley,et al.  Fuzzy differential equations , 2000, Fuzzy Sets Syst..

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

[3]  Caroline M. Eastman,et al.  Review: Introduction to fuzzy arithmetic: Theory and applications : Arnold Kaufmann and Madan M. Gupta, Van Nostrand Reinhold, New York, 1985 , 1987, Int. J. Approx. Reason..

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

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

[6]  Jiqing Qiu,et al.  Global existence of solutions for fuzzy second-order differential equations under generalized H-differentiability , 2010, Comput. Math. Appl..

[7]  Y. Chalco-Cano,et al.  Fuzzy differential equations with generalized derivative , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

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

[9]  Yurilev Chalco-Cano,et al.  Generalized derivative and π-derivative for set-valued functions , 2011, Inf. Sci..

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

[11]  Tofigh Allahviranloo,et al.  Toward the existence and uniqueness of solutions of second-order fuzzy differential equations , 2009, Inf. Sci..

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

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

[14]  V LUPULESCU.  Initial value problem for fuzzy differential equations under dissipative conditions , 2008, Inf. Sci..