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Existence results for fractional order semilinear functional differential equations with nondense domain. (English) Zbl 1179.26018
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:
26A33Fractional derivatives and integrals (real functions)
26A42Integrals of Riemann, Stieltjes and Lebesgue type (one real variable)
34G25Evolution inclusions