Boundary value problems for differential inclusions with fractional order

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1. [1] J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin-Heidelberg, New York, 1984. Zbl0538.34007
2. [2] J.P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, 1990. 
3. [3] A. Belarbi, M. Benchohra, S. Hamani and S.K. Ntouyas, Perturbed functional differential equations with fractional order, Commun. Appl. Anal. 11 (3-4) (2007), 429-440. Zbl1148.34042
4. [4] A. Belarbi, M. Benchohra and A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Appl. Anal. 85 (2006), 1459-1470. Zbl1175.34080
5. [5] M. Benchohra, S. Hamani and S.K. Ntouyas, Boundary value problems for differential equations with fractional order, Surv. Math. Appl. 3 (2008), 1-12. Zbl1157.26301
6. [6] M. Benchohra, J. Henderson, S.K. Ntouyas and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2) (2008), 1340-1350. Zbl1209.34096
7. [7] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. 
8. [8] H. Covitz and S. B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11. Zbl0192.59802
9. [9] K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin-New York, 1992. 
10. [10] D. Delbosco and L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl. 204 (1996), 609-625. Zbl0881.34005
11. [11] K. Diethelm and A.D. Freed, On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, in: 'Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties' (F. Keil, W. Mackens, H. Voss and J. Werther, Eds), pp. 217-224, Springer-Verlag, Heidelberg, 1999. 
12. [12] K. Diethelm and N.J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl. 265 (2002), 229-248. Zbl1014.34003
13. [13] K. Diethelm and G. Walz, Numerical solution of fractional order differential equations by extrapolation, Numer. Algorithms 16 (1997), 231-253. Zbl0926.65070
14. [14] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003. Zbl1025.47002
15. [15] A.M.A. El-Sayed, Fractional order evolution equations, J. Fract. Calc. 7 (1995), 89-100. 
16. [16] A.M.A. El-Sayed, Fractional order diffusion-wave equations, Intern. J. Theoretical Physics 35 (1996), 311-322. 
17. [17] A.M.A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (1998), 181-186. Zbl0934.34055
18. [18] A.M.A. El-Sayed and A.G. Ibrahim, Multivalued fractional differential equations, Appl. Math. Comput. 68 (1995), 15-25. Zbl0830.34012
19. [19] L. Gaul, P. Klein and S. Kempfle, Damping description involving fractional operators, Mech. Systems Signal Processing 5 (1991), 81-88. 
20. [20] W.G. Glockle and T.F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophys. J. 68 (1995), 46-53. 
21. [21] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Theory I, Kluwer, Dordrecht, 1997. 
22. [22] N. Heymans and I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives, Rheologica Acta 45 (5) (2006), 765-772. 
23. [23] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. Zbl0998.26002
24. [24] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991. 
25. [25] A.A. Kilbas and S.A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions, Differential Equations 41 (2005), 84-89. Zbl1160.34301
26. [26] A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006. Zbl1092.45003
27. [27] V. Lakshmikantham and J.V. Devi, Theory of fractional differential equations in a Banach space, Eur. J. Pure Appl. Math. 1 (1) (2008), 38-45. Zbl1146.34042
28. [28] F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in: 'Fractals and Fractional Calculus in Continuum Mechanics' (A. Carpinteri and F. Mainardi, Eds), pp. 291-348, Springer-Verlag, Wien, 1997. Zbl0917.73004
29. [29] F. Metzler, W. Schick, H.G. Kilian and T.F. Nonnenmacher, Relaxation in filled polymers: A fractional calculus approach, J. Chem. Phys. 103 (1995), 7180-7186. 
30. [30] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993. Zbl0789.26002
31. [31] K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, London, 1974. Zbl0292.26011
32. [32] A. Ouahab, Some results for fractional boundary value problem of differential inclusions, Nonlinear Anal. (2007), doi:10.1016/j.na.2007.10.021. Zbl1169.34006
33. [33] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. 
34. [34] I. Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. Calculus Appl. Anal. 5 (2002), 367-386. Zbl1042.26003
35. [35] I. Podlubny, I. Petraš, B.M. Vinagre, P. O'Leary and L. Dorčak, Analogue realizations of fractional-order controllers. Fractional order calculus and its applications, Nonlinear Dynam. 29 (2002), 281-296. Zbl1041.93022
36. [36] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993. 
37. [37] K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin, 1980. 
38. [38] C. Yu and G. Gao, Existence of fractional differential equations, J. Math. Anal. Appl. 310 (2005), 26-29. Zbl1088.34501

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