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The global existence of nonlinear evolutionary equation with small delay. (English) Zbl 1251.34013
Summary: We investigate the global existence of the delayed nonlinear evolutionary equation $$\partial_t u + Au = f(u(t), u(t - \tau))$$ . Our work space is the fractional powers space $$X^a$$. Under the fundamental theorem on sectorial operators, we make use of the fixed-point principle to prove the local existence and uniqueness theorem. Then, the global existence is obtained by Gronwall’s inequality.
##### MSC:
 34A08 Fractional ordinary differential equations
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##### References:
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