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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:
45N05Abstract integral equations, integral equations in abstract spaces
45G10Nonsingular nonlinear integral equations
26A33Fractional derivatives and integrals (real functions)
45J05Integro-ordinary differential equations
45K05Integro-partial differential equations
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References:
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