Mild solutions for class of neutral fractional functional differential equations with not instantaneous impulses. (English) Zbl 1390.34221
Summary: This article contains the existence results of the mild solutions of an abstract semilinear neutral fractional differential equations with not instantaneous impulses. The results are proved by using the theory of analytic \(\alpha\)-resolvent family and fixed point theorems. One application involving partial differential equations with impulses are presented.
MSC:
| 34K37 | Functional-differential equations with fractional derivatives |
| 34K40 | Neutral functional-differential equations |
| 34K45 | Functional-differential equations with impulses |
| 47N20 | Applications of operator theory to differential and integral equations |
| 34A37 | Ordinary differential equations with impulses |
| 34K30 | Functional-differential equations in abstract spaces |
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