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Existence results for impulsive neutral differential and integrodifferential equations with nonlocal conditions via fractional operators. (English) Zbl 1200.34095
The authors consider a class of first order impulsive neutral differential equations as well as a class of first order impulsive neutral integrodifferential equations, both governed by nonlinear perturbations of a densely defined and closed linear operator generating an analytic compact semigroup, and subjected to nonlocal initial conditions. By imposing some technical conditions on the data and using Sadovskii’s fixed point theorem, they prove some existence results which cover the case when the nonlinear part is defined on a fractional power of the linear part. An illustrative example is included.
34K45Functional-differential equations with impulses
34K40Neutral functional-differential equations
34K30Functional-differential equations in abstract spaces
47D06One-parameter semigroups and linear evolution equations
47N20Applications of operator theory to differential and integral equations