EXISTENCE OF SOLUTIONS FOR FRACTIONAL SEMILIEAR EVOLUTION BOUNDARY VALUE PROBLEM

[1] B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Analysis: Hybrid Systems (2009), (doi:10.1016/j.nahs. 2009.01.008).
[2] A. Anguraj, P. Karthikeyan, G. M. N’Guerekata, Nonlocal Cauchy problem for some fractional abstract integrodifferential equations in Banach space, Commn. Math. Anal. v. 6 (2009), 1–6.
[3] K. Balachandran, J. Y. Park, Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear Analysis, TMA (2009), (doi:10.1016/j.na.2009.03.005).
[4] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991) 494–505.
[5] M. Caputo, Linear models of dissipation whose q is almost frequently independent, Part II, J. Roy. Astr. Soc. 13(1967) 529–539.
[6] D. Delbosco and L. Rodino, Existence and uniqueness for a nolinear fractional differential equation, J. Math. Anal. Appl. 204 (1996), 609–625.
[7] K. Diethelm and N. J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl. 265 (2002), 229–248.
[8] I.H. Dimovski, V.S. Kiryakova, On an integral transformation , due to N. Obrechkoff, In: Lect. Notes Math. 798 (1980), 141–147
[9] M. M. El-Borai, Semigroups and some nonlinear fractional differential equations, Applied Mathematics and Computation, 149 (2004) 823–831.
[10] A. M. A. El-Sayed, Fractional order evolution equations, J. Fract. Calc. 7 (1995), 89–100.
[11] W. G. Glockle and T. F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophys. J. V. 68 (1995), 46–53.
[12] G. M. N’Guerekata, A Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear Analysis, 70 (2009), 1873–1876.
[13] G. M. N’Guerekata, Existence and uniqueness of an integral solution to some Cauchy Problem with nonlocal conditions, Differential and Difference Equations and Applications, 843-849, Hindawi Publ.,Corp, New York, 2006.
[14] J. H. He, Some applications of nonlinear fractional differential equations and their approximation, Bull. Sci. Technol. 15(2) (1999), 86–90.
[15] J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mec. Engrg. 167 (1998), 57–68.

[16] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
[17] O. K. Jaradat, A. Al-Omari and S. Momani, Existence of the mild solution for fractional semilinear initial value problem, Nonlinear Analysis, 69 (2008), 3153–3159.
[18] A. A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations. Volume 204 (North-Holland Mathematics Studies) 2006.
[19] V. Lakshmikantham, Theory of fractional differential equations, Nonlinear Anal. TMA (in press) (doi:10.1016/j.na 2007.0.025)
[20] V. Lakshmikantham, J. Vasundhara Devi, Theory of fractional differential equations in Banach spaces, European J. Pure and App. Math. 1 (2008), 38–45.
[21] V. Lakshmikantham, A. S. Vatsala, Basic theory of fractional differential equations, Nonlinear Analysis, 69 (2008), 2677–2682.
[22] G. M. Mophou, G. M. N’Gu ́er ́ekata, Mild solutions to semilinear fractional diferential equations, Elec. J. Diff. Eqn. No. 21 (2009), 1–9.
[23] G. M. Mophou, G. M. N’Guerekata, Existence of the mild solutions for some fractional differential equations with nonlocal conditions. Semigroup Forum (online first).
[24] I. Podlubny, Fractional Differential Equations, San Diego Academic Press, New York, 1999.
[25] A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer - Verlag, New York, 1983.
[26] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and derivatives, Theory and Applications, Gordon and Breach Yverden, 1993.
[27] B. N. Sadovskii, On a fixed point principle, Funct. Anal. Appl. 1(1967), 74–76.
[28] L. Wei, Global existence and chaos control of fractional differential equations. J. Math. Anal. Appl. 332 (2007), 709–726.
[29] S. Zhang, Positive solutions for boundary-value problems for nonlinear fractional differential equations. Elec. J. Diff. Eqn. 36 (2006), 1–12.