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Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays. (English) Zbl 1184.45006

The authors establish the existence and uniqueness of a mild solution to a semilinear fractional integro-differential equation with delay and nonlocal initial conditions in general Banach spaces. The derivatives are understood in the Riemann-Liouville sense.

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45G10 Other nonlinear integral equations
26A33 Fractional derivatives and integrals
45J05 Integro-ordinary differential equations
45K05 Integro-partial differential equations
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