On the existence of mild solutions to some semilinear fractional integro-differential equations
T. Diagana, Howard University, Washington, DC, U.S.A. E. J. Qualitative Theory of Diff. Equ., No. 58. (2010), pp. 1-17.
G. M. Mophou, Universite des Antilles et de La Guyane, Campus Fouillole, Guadeloupe
G. M. N'Guérékata, Morgan State University, E. Cold Spring Lane, Baltimore, MD, U.S.A.
| Communicated by M. Benchohra. | Received on 2010-05-19 Appeared on 2010-09-23 |
Abstract: This paper deals with the existence of a mild solution for some fractional semilinear differential equations with non local conditions. Using a more appropriate definition of a mild solution than the one given in [12], we prove the existence and uniqueness of such solutions, assuming that the linear part is the infinitesimal generator of an analytic semigroup that is compact for $t > 0$ and the nonlinear part is a Lipschitz continuous function with respect to the norm of a certain interpolation space. An example is provided.
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