Almost automorphic solutions to a class of semilinear fractional differential equations
نویسندگان
چکیده
We study almost automorphic (mild) solutions of the semilinear fractional equation ∂ t u = Au + ∂ α−1 t f(·, u), 1 < α < 2, considered in a Banach space X, where A is a linear operator of sectorial type ω < 0. We prove the existence and uniqueness of an almost automorphic mild solution assuming f(t, x) is almost automorphic in t for each x ∈ X, satisfies some Lipschitz type conditions and takes values on X.
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ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 21 شماره
صفحات -
تاریخ انتشار 2008