Solving fuzzy fractional differential equations by fuzzy Laplace transforms

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 3, 2012, Pages 1372-1381

  Salahshour, S ^a   Allahviranloo, T ^b   Abbasbandy, S ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Fuzzy fractional differential equations; Fuzzy Laplace transforms; Riemann Liouville H differentiability

Indexed keywords

LIOUVILLE EQUATION;

FRACTIONAL DIFFERENTIAL EQUATIONS; FUZZY FRACTIONAL DIFFERENTIAL EQUATION; FUZZY LAPLACE TRANSFORM; H-DIFFERENTIABILITY; LAPLACE TRANSFORM METHOD; LIOUVILLE; RIEMANN-LIOUVILLE H-DIFFERENTIABILITY;

LAPLACE TRANSFORMS;

EID: 80053384834     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.07.005     Document Type: Article

References (36)

1. Abbasbandy S., Shirzadi A. Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems. Numer Algor 2010, 54:521-532.
2. Allahviranloo T., Abbasbandy S., Salahshour S., Hakimzadeh A. A new method for solving fuzzy linear differential equations. Computing 2011, 92:181-197.
3. Allahviranloo T., Salahshour S. A new approach for solving first order fuzzy differential equations. Commun Comput Inform Sci 2010, 81:522-531. Part 5, Part 7.
4. Allahviranloo T., Salahshour S. Euler method for solving hybrid fuzzy differential equation. Soft Comput 2011, 15:1247-1253.
5. Allahviranloo T., Ahmadi M.B. Fuzzy Laplace transforms. Soft Comput 2010, 14:235-243.
6. Allahviranloo T, Salahshour S, Abbasbandy S. Explicit solutions of fractional differential equations with uncertainty. Soft Comput. doi:10.1007/s00500-011-0743-y.
7. Agarwal R.P., Lakshmikantham V., Nieto J.J. On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal 2010, 72:2859-2862.
8. Arara A., Benchohra M., Hamidi N., Nieto J.J. Fractional order differential equations on an unbounded domain. Nonlinear Anal 2010, 72:580-586.
9. Arshad S., Lupulescu V. On the fractional differential equations with uncertainty. Nonlinear Anal 2011, 74:3685-3693.
10. Babenko YI. Heat and Mass Transfer, Chemia, Leningrad; 1986.
11. Bagley R.L. On the fractional order initial value problem and its engineering applications. Fractional calculus and its applications 1990, 12-20. College of Engineering, Nihon University, Tokyo. K. Nishimoto (Ed.).
12. Bede B., Gal S.G. Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst 2005, 151:581-599.
13. Bede B., Rudas I.J., Bencsik A.L. First order linear fuzzy differential equations under generalized differentiability. Inform Sci 2007, 177:1648-1662.
14. Beyer H., Kempfle S. Definition of physically consistent damping laws with fractional derivatives. ZAMM 1995, 75:623-635.
15. Diethelm K., Ford N.J. Analysis of fractional differential equations. J Math Anal Appl 2002, 265:229-248.
16. Friedman M., Ma M., Kandel A. Numerical solution of fuzzy differential and integral equations. Fuzzy Sets Syst 1999, 106:35-48.
17. Khastan A, Nieto JJ. Rosana Rodriguez-Lopez, Variation of constant formula for first order fuzzy differential equations. Fuzzy Sets Syst; in press, doi:10.1016/j.fss.2011.02.020.
18. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations 2006, Elsevier Science B.V, Amesterdam.
19. Lakshmikantham V., Leela S., Vasundhara Devi J. Theory of fractional dynamic systems 2009, Cambridge Scientific Pub, Cambridge, UK.
20. Lakshmikantham V., Mohapatra R.N. Theory of fuzzy differential equations and applications 2003, Taylor & Fracncis, London.
21. Lakshmikantham V., Vatsala A.S. Basic theory of fractional differential equations. Nonlinear Anal 2008, 69:2677-2682.
22. Ma M., Friedman M., Kandel A. Numerical solution of fuzzy differential equations. Fuzzy Sets Syst 1999, 105:133-138.
23. Nieto J.J., Rodroguez-Lopez R., Franco D. Linear first-order fuzzy differential equations. Int J Uncertainty Fuzziness Knowledge-Based Syst 2006, 14:687-709.
24. Nieto J.J. Maximum principles for fractional differential equations derived from Mittag-Leffler functions. Appl Math Lett 2010, 23:1248-1251.
25. Perfilieva I. Fuzzy transforms: theory and applications. Fuzzy Sets Syst 2006, 157:993-1023.
26. Perfilieva I, De Meyer H, De Baets B, Cauchy problem with fuzzy initial condition and its approximate solution with the help of fuzzy transform, WCCI 2008. In: Proceedings 978-1-4244-1819-0- Hong Kong IEEE Computational Intelligence Society; 2008, p. 2285-2290.
27. Podlubny I. Fractional differential equation 1999, Academic Press, San Diego.
28. Puri M.L., Ralescu D. Fuzzy random variables. J Math Anal Appl 1986, 114:409-422.
29. Salahshour S., Haghi E. Solving fuzzy heat equation by fuzzy Laplace transforms. Commun Comput Inform Sci 2010, 81:512-521. Part 5, Part 7.
30. Stefanini L. A generalization of Hukuhara difference and division for interval and fuzzy arithmetic. Fuzzy Sets Syst 2010, 161. p. 1564-158.
31. Stefanini L., Bede B. Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Anal: TMA 2009, 71:1311-1328.
32. Wu H.C. The improper fuzzy Riemann integral and its numerical integration. Inform Sci 1999, 111:109-137.
33. Xu J., Liao Z., Hu Z. A class of linear differential dynamical systems with fuzzy initial condition. Fuzzy Sets Syst 2007, 158:2339-2358.
34. Xu J., Liao Z., Nieto J.J. A class of linear differential dynamical systems with fuzzy matrices. J Math Anal Appl 2010, 368:54-68.
35. Zhu Y. Stability analysis of fuzzy linear differential equations. Fuzzy Optim Decision Making 2010, 9:169-186.
36. Zimmermann H.J. Fuzzy set theory and its applications 1991, Kluwer Academi Publishers, Dordrecht.