Impulsive fractional semilinear integrodifferential equations with nonlocal conditions. (English) Zbl 1471.45007
Summary: This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. Furthermore, the uniqueness of PC-mild solutions is proved in the case of the noncompact resolvent operator.
MSC:
| 45J05 | Integro-ordinary differential equations |
| 34K37 | Functional-differential equations with fractional derivatives |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
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