REFERENCES
[1] R. P. Agarwal, M. Benchohra and S. Hamani, Boundary value problems for differential inclusions
with fractional order, Adv. Stud. Contemp. Math. 12 (2008), 181–196.
[2] R. P. Agarwal, M. Benchohra and S. Hamani, Boundary value problems for fractional differential
equations, Georgian Math. J. (to appear).
[3] R. P. Agarwal, M. Meehan and D. O’Regan, Fixed Point Theory and Applications, Cambridge
Tracts in Mathematics, 141, Cambridge University Press, Cambridge, 2001.
[4] R. R. Akhmerov, M. I. Kamenskii, A. S. Patapov, A. E. Rodkina and B. N. Sadovskii, Measures
of Noncompactness and Condensing Operators, trans. from the Russian by A. Iacob, Birkhauser Verlag, Basel, 1992.
[5] J. C. Alv`arez, Measure of noncompactness and fixed points of nonexpansive condensing mappings
in locally convex spaces, Rev. Real. Acad. Cienc. Exact. Fis. Natur. Madrid 79 (1985), 53–66.
[6] J. Bana`s, Applications of measures of weak noncompactness and some classes of operators in
the theory of functional equations in the Lebesgue space, Nonlinear Anal. 30 (1997), 3283–3293.
[7] J. Bana`s and B. C. Dhage, Global asymptotic stability of solutions of a fractional integral
equation, Nonlinear Anal. 69 (2008) 1945–1952.
[8] J. Bana`s and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in
Pure and Applied Mathematics, Volume 60, Marcel Dekker, New York, 1980.
[9] J. Bana`s and L. Olszowy, Measures of noncompactness related to monotonicity, Comment.
Math. 41 (2001), 13–23.
[10] J. Bana`s and B. Rzepka, An application of a measure of noncompactness in the study of
asymptotique stability, Appl. Math. Lett. 16 (2003), 1–6.
[11] J. Bana`s and K. Sadarangani, On some measures of noncompactness in the space of continuous
functions, Nonlinear Anal. 68 (2008), 377–383.
[12] A. Belarbi, M. Benchohra and A. Ouahab, Existance results for functional differential equations
of fractional order, Appl. Anal. 85 (2006), 1459–1470.
[13] M. Benchohra, S. Hamani and S. K. Ntouyas, Boundary value problems for differential equations
with fractional order, Surveys Math. Appl. 3 (2008), 1–12.
[14] 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. 332 (2008), 1340–1350.
[15] D. Delboso and L. Rodino, Existence and uniqueness for a nonlinear fractional differential
equation, J. Math. Anal. Appl. 204 (1996), 609–625.
[16] K. Diethelm and N. J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl. 265 (2002), 229–248.
[17] A. M. A. El-Sayed, W. G. El-Sayed and O.L. Moustafa, On some fractional functional equations,
Pure Math. Appl. 6 (1995), 321–332.
[18] W. G. El-Sayed and B. Rzepka, Nondecreasing solutions of a quadratic integral equation of
Urysohn type, Computers Math. Appl. 51 (2006) 1065–1074.
[19] K. M. Furati and N.-eddine Tatar, An existence result for a nonlocal fractional differential
problem, J. Fractional Calc. 26 (2004), 43–51.
[20] K. M. Furati and N.-eddine Tatar, Behavior of solutions for a weighted Cauchy-type fractional
differential problem, J. Fractional Calc. 28 (2005), 23–42.
[21] K. M. Furati and N.-eddine Tatar, Power type estimates for a nonlinear fractional differential
equation, Nonlinear Anal. 62 (2005), 1025–1036.
[22] L. Gaul, P. Klein and S. Kempfle, Damping description involving fractional operators, Mech.
Systems Signal Processing 5 (1991), 81–88.
[23] W. G. Glockle and T. F. Nonnenmacher, A fractional calculus approach of self-similar protein
dynamics, Biophys. J. 68 (1995), 46–53.
[24] D. Guo, V. Lakshmikantham and X. Liu, Nonlinear Integral Equations in Abstract Spaces,
Mathematics and its Applications, 373, Kluwer Academic Publishers Group, Dordrecht, 1996.
[25] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
[26] A. A. Kilbas, H. M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential
Equations, North Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
[27] V. Lakshmikantham and J. V. Devi, Theory of fractional differential equations in a Banach
space, Eur. J. Pure Appl. Math. 1 (2008), 38–45.
[28] F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics,
in: “Fractals and Fractional Calculus in Continuum Mechanics” (A. Carpinteri, F. Mainardi
Eds.), Springer-Verlag, Wien, 1997, pp. 291–348.
[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] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations,
John Wiley, New York, 1993.
[31] S. M. Momani and S. B. Hadid, Some comparison results for integro-fractional differential
inequalities, J. Fract. Calc. 24 (2003), 37–44.
[32] S. M. Momani, S. B. Hadid and Z. M. Alawenh, Some analytical properties of solutions of
differential equations of noninteger order, Int. J. Math. Math. Sci. 2004, no. 13-16, 697–701.
[33] H. M¨onch, Boundary value problems for nonlinear ordinary differential equations of second
order in Banach spaces, Nonlinear Anal. 4 (1980), 985–999.
[34] H. M¨onch and G. F. Von Harten, On the Cauchy problem for ordinary differential equations
in Banach spaces, Archiv. Math. Basel 39 (1982), 153–160.
[35] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, vol.
198, Academic Press, San Diego, 1999.
[36] S. Szufla, On the application of measure of noncompactness to existence theorems, Rend. Sem.
Mat. Univ. Padova 75 (1986), 1–14.
[37] S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential
equations, Electron. J. Differential Equations 2006, No. 36, 12 pp. (electronic).