Laplace transform formula on fuzzy nth-order derivative and its application in fuzzy ordinary differential equations

In this paper, the Laplace transform formula on the fuzzy nth-order derivative by using the strongly generalized differentiability concept is investigated. Also, the related theorems and properties are proved in detail and, it is used in an analytic method for fuzzy two order differential equation. The method is illustrated by solving some examples.

[1]  Paul P. Wang,et al.  Fuzzy sets : theory and applications to policy analysis and information systems , 1981 .

[2]  Tofigh Allahviranloo,et al.  Euler method for solving hybrid fuzzy differential equation , 2011, Soft Comput..

[3]  Soheil Salahshour.  Nth-order Fuzzy Differential Equations Under Generalized Differentiability , 2011 .

[4]  Soheil Salahshour,et al.  Solving Fuzzy Heat Equation by Fuzzy Laplace Transforms , 2010, IPMU.

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

[6]  Omid Solaymani Fard,et al.  Numerical solutions for linear system of first-order fuzzy differential equations with fuzzy constant coefficients , 2011, Inf. Sci..

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

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

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

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

[11]  Kevin D. Reilly,et al.  Simulating continuous fuzzy systems , 2005, Inf. Sci..

[12]  A. Kandel.  Fuzzy Dynamical Systems and the Nature of Their Solutions , 1980 .

[13]  P. Kloeden.  Remarks on Peano-like theorems for fuzzy differential equations , 1991 .

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

[15]  Saeid Abbasbandy,et al.  NUMERICAL METHODS FOR FUZZY DIFFERENTIAL INCLUSIONS , 2004 .

[16]  Juan J. Nieto,et al.  Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses , 2011, Fuzzy Optim. Decis. Mak..

[17]  George A. Anastassiou.  A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE , 2010 .

[18]  Saeid Abbasbandy,et al.  Numerical methods forfuzzy differential inclusions , 2004 .

[19]  Tofigh Allahviranloo,et al.  Difference Methods for Fuzzy Partial Differential Equations , 2002 .

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

[21]  James J. Buckley,et al.  Introduction to fuzzy partial differential equations , 1999, Fuzzy Sets Syst..

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

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

[24]  A. Kandel,et al.  NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS , 1999 .

[25]  Saeid Abbasbandy,et al.  Numerical Solutions of Fuzzy Differential Equations by Taylor Method , 2002 .

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

[27]  Sahin Emrah Amrahov,et al.  A new approach to fuzzy initial value problem , 2013, Soft Computing.

[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]  Sahin Emrah Amrahov,et al.  Solution of linear differential equations with fuzzy boundary values , 2014, Fuzzy Sets Syst..

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

[31]  Tofigh Allahviranloo,et al.  Solving fuzzy differential equations by differential transformation method , 2009, Inf. Sci..

[32]  O. He,et al.  On fuzzy differential equations , 1989 .

[33]  D. Dubois,et al.  Towards fuzzy differential calculus part 1: Integration of fuzzy mappings , 1982 .

[34]  Abraham Kandel,et al.  Numerical solutions of fuzzy differential equations , 1999, Fuzzy Sets Syst..

[35]  T Allahviranloo,et al.  NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATION BY TAILOR METHOD , 2002 .

[36]  Hsien-Chung Wu,et al.  The fuzzy Riemann integral and its numerical integration , 2000, Fuzzy Sets Syst..

[37]  Tofigh Allahviranloo,et al.  Fuzzy Laplace transforms , 2009, Soft Comput..

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

[39]  Bernard De Baets,et al.  Analytical and numerical solutions of fuzzy differential equations , 2013, Inf. Sci..

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

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

[42]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[43]  Abraham Kandel,et al.  Numerical solutions of fuzzy differential and integral equations , 1999, Fuzzy Sets Syst..

[44]  Maryam Mosleh,et al.  Simulation and evaluation of fuzzy differential equations by fuzzy neural network , 2012, Appl. Soft Comput..

[45]  W. Menda.  LINEAR FUZZY DIFFERENTIAL EQUATION SYSTEMS ON R1 , 1988 .

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

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

[48]  M. Ghanbari,et al.  NUMERICAL SOLUTION OF FUZZY INITIAL VALUE PROBLEMS UNDER GENERALIZED DIFFERENTIABILITY BY HPM , 2009 .

[49]  A. Kandel,et al.  Fuzzy Differential Equations , 2019, Modeling and Control of Uncertain Nonlinear Systems with Fuzzy Equations and Z‐Number.

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

[51]  Tofigh Allahviranloo,et al.  Applications of fuzzy Laplace transforms , 2013, Soft Comput..