Abstract

In this paper, we consider the well-posedness and approximation for nonhomogeneous fractional differential equations in Banach spaces E. Firstly, we get the necessary and sufficient condition for the well-posedness of nonhomogeneous fractional Cauchy problems in the spaces $C_0^{\beta }([0,T];E).$ Secondly, by using implicit difference scheme and explicit difference scheme, we deal with the full discretization of the solutions of nonhomogeneous fractional differential equations in time variables, get the stability of the schemes and the order of convergence.

中文翻译：

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非齐次分数阶微分方程的适定性和近似

摘要

在本文中，我们考虑了 Banach 空间E中非齐次分数阶微分方程的适定性和近似性。首先，我们得到了空间中非齐次分数柯西问题适定性的充要条件$C_0^{\beta }([0,吨];乙).$ 其次，利用隐式差分格式和显式差分格式，对非齐次分数阶微分方程在时间变量中的解进行完全离散化处理，得到格式的稳定性和收敛阶次。