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Zbl 1179.26018
Belmekki, Mohammed; Benchohra, Mouffak
Existence results for fractional order semilinear functional differential equations with nondense domain. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, A, 925-932 (2010). ISSN 0362-546X

Summary: We establish sufficient conditions for existence and uniqueness of solutions for some nondensely defined semilinear functional differential equations involving the Riemann-Liouville derivative. Our approach is based on integrated semigroup theory, the Banach contraction principle, and the nonlinear alternative of Leray-Schauder type.

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
26A42 Ordinary integrals of functions of one real variable
34G25 Evolution inclusions

Keywords: semilinear functional differential equation; nondense domain; fractional derivative; fractional integral; fixed point; semigroups; integral solutions

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