Equations in Banach spaces with a degenerate operator under a fractional derivative

被引：0
作者：
V. E. Fedorov
D. M. Gordievskikh
M. V. Plekhanova
机构：
[1] Chelyabinsk State University,
[2] South Ural State University (National Research University),undefined
来源：
Differential Equations | 2015年 / 51卷
关键词：
Banach Space; Cauchy Problem; Fractional Derivative; Convex Space; Caputo Fractional Derivative;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study an inhomogeneous linear fractional differential equation in a Banach space with a degenerate operator under the derivative. In the case of relative p-boundedness of the pair of operators in the equation, we prove the unique solvability of the Cauchy and Showalter problems for it and represent the solution via operator functions of the Mittag-Leffler type. The abstract results obtained are used to study a class of initial–boundary value problems for partial differential equations of arbitrary fractional order with respect to time.
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页码：1360 / 1368
页数：8
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