Fuzzy fractional differential equations under generalized fuzzy Caputo derivative

Journal of Intelligent and Fuzzy Systems

Volumn 26, Issue 3, 2014, Pages 1481-1490

  Allahviranloo, T ^a   Armand, A ^a   Gouyandeh, Z ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Fuzzy Caputo fractional differential equations (FCFDEs); Generalized Hukuhara differentiability; Krasnoselskii Krein condition

Indexed keywords

EID: 84884844153     PISSN: 10641246     EISSN: 18758967     Source Type: Journal    
DOI: 10.3233/IFS-130831     Document Type: Article

References (28)

1. R.P. Agarwal, V. Lakshmikantham and J.J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal 72 (2010), 59-62.
2. T. Allahviranloo, N.A. Kiani and M. Barkhordari, Toward the existence and uniqueness of solutions of second-order fuzzy differental equations, Inf Sci 179 (2009), 1207-1215.
3. T. Allahviranloo, S. Abbasbandy and S. Salahshour, Fuzzy fractional differential equations with Nagumo and Krasnoselskii-Krein condition, In: EUSFLAT-LFA 2011, Aixles-Bains, France, 2011.
4. T. Allahviranloo, S. Salahshour and S. Abbasbandy, Explicit solutions of fractional differential equations with uncertainty, Soft Comput Fus Found Meth Appl 16 (2012), 297-302.
5. T. Allahviranloo and S. Gholami, Note on "Generalized Hukuhara differentiability of interval-valued functions and interval differential equations", Journal of Fuzzy Set Valued Analysis 2012 (2012), 1-4.
6. S. Arshad andV. Lupulescu, On the fractional differential equations with uncertainty, Nonlinear Anal 74 (2011), 85-93.
7. S. Arshad andV. Luplescu, fractional differential equation with fuzzy initial conditon, Electronic Journal of Differential Equations 34 (2011), 1-8.
8. B. Bede, I.J. Rudas and A.L. Bencsik, First order linear fuzzy differential equations under generalized differentiability, Inf Sci 177 (2006), 1648-1662.
9. B. Bede and S. Gal, Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems 151 (2005), 581-599.
10. B. Bede and L. Stefanini, Generalized differentiability of fuzzyvalued functions, Fuzzy Sets and Systems (2012). In press
11. T. Gnana Bhaskar,V. Lakshmikantham and S. Leela, Fractional differential equations with a Krasnoselskii-Krein-type conditions, Nonlinear Analysis: Hybrid System 3 (2009), 734-737.
12. K. Diethelm and G. Gesellschaft, The Analysis of Fractional Differential Equations, Springer Heidelberg, Dordrecht, London, New York.
13. K. Diethelm, The Analysis of Fractional Differential Equations (An Application-Oriented Exposition Using Differential Operators of Caputo Type), Lecture Notes in Mathematics, Springer-Verlag Berlin Heidelberg, 2004.
14. D. Dubois and H. Prade, Towards fuzzy differential calculuspart 1, Fuzzy Sets and Systems 8 (1982), 1-17.
15. D. Dubois and H. Prade, Towards fuzzy differential calculuspart 2, Fuzzy Sets and Systems 8 (1982), 105-116.
16. D. Dubois and H. Prade, Towards fuzzy differential calculuspart 3, Fuzzy Sets and Systems 8 (1982), 225-234.
17. A. Khastan and J.J. Nieto,Aboundary value problem for second order fuzzy differential equations, Nonlinear Anal 72 (2010), 3583-3593.
18. V. Lakshmikantham and J. Vasundhara Devi, Theory of fractional differential equations in a Banach Space, European Journal of Pure and Applied Mathematics 1 (2008), 38-45.
19. V. Lupulescu, On a class of fuzzy functional differential equations, Fuzzy Sets and Systems 160 (2009), 1547-1562.
20. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, JohnWiley and Sons, Inc, New York, 1993.
21. C.V. Negoita and D.A. Ralescu, Applications of fuzzy sets to system analysis, Birkhauser, Basel, 1975.
22. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
23. M.L. Puri and D.A. Ralescu, Differentials for fuzzy functions, J Math Anal Appl 91 (1983), 552-558.
24. M.L. Puri and D.A. Ralescu, Fuzzy random variables, J Math Anal Appl 114 (1986), 409-422.
25. S. Salahshour, T. Allahviranloo and S. Abbasbandy, Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun Nonlinear Sci Numer Simulat 17 (2012), 1372-1381.
26. Sh. Shahriari, Approximately calculus, American Mathematical Soc, 2006.
27. L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis 71 (2009), 1311-1328.
28. J. Xu, Z. Liao and J.J. Nieto, A class of linear differential dynamical systems with fuzzy matrices, J Math Anal Appl 368 (2010), 54-68.