Abstract:A linear th order (Riemann-Liouville) fractional differential equation with initial values, together with a suitable assumption, is proved to be equivalent to a Volterra integral equation of the second kind involving an th order (Riemann-Liouville) fractional integral operator. Two special cases of the result are given: one shows that a well-known result on the solution of an th order fractional differential equation needs an additional condition to hold, and another strengthens a previous result on an th order fractional integral operator composed with an th order fractional differential operator.

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中文翻译：

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高阶线性Riemann-Liouville分数阶微分方程和积分方程的等价性

摘要：证明了具有初始值的线性th阶（Riemann-Liouville）分数阶微分方程和适当的假设等效于包含th阶（Riemann-Liouville）分数阶积分算子的第二类Volterra积分方程。给出了两种特殊情况的结果：一种表明已知的三阶分数阶微分方程解的结果需要附加的条件成立，另一种增强了由三阶分数阶微分算子构成的先前结果。阶分数阶微分算子。

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