In a Banach space, the inverse source problem for a fractional differential equation with Caputo–Dzhrbashyan derivative is considered. The initial and observation conditions are given by elements from D⁢(A){D(A)}, and the operator function on the right side is sufficiently smooth. Two types of the observation operator are considered: integral and at the final point. Under the assumptions that operator A is a generator of positive and compact semigroup the uniqueness, existence and stability of the solution are proved.

中文翻译：

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抽象分数阶微分方程的逆源问题

在Banach空间中，考虑了具有Caputo–Dzhrbashyan导数的分数阶微分方程的逆源问题。初始条件和观察条件由D⁢（A）{D（A）}中的元素给出，并且右侧的算子函数足够平滑。考虑两种类型的观测算子：积分算子和终点算子。在算子A为正和紧半群的生成子的假设下，证明了解的唯一性，存在性和稳定性。