Abstract We construct a fundamental solution for an ordinary differential equation with a distributed-order differentiation operator. The properties of the solution are studied. A Lagrange formula is obtained for distributed-order differential operators. A well-posed form of the Cauchy problem is found for the equation in question, and the solution of the problem is written using the Lagrange formula.

中文翻译：

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具有分布阶微分算子的常微分方程的柯西问题

摘要 我们用分布阶微分算子构造常微分方程的基本解。研究了溶液的性质。获得了分布式阶微分算子的拉格朗日公式。为所讨论的方程找到柯西问题的适定形式，并使用拉格朗日公式写出问题的解。