Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

中文翻译：

---

Mkhitar Djrbashian 及其对分数阶微积分的贡献

摘要 本调查论文致力于描述MM Djrbashian 与现代分数微积分理论相关的结果。MM Djrbashian (1918-1994) 是著名的复分析、调和分析和近似理论专家。无论如何，他对分数阶微积分、分数阶算子的边值问题、分数阶微积分皇后函数（Mittag-Leffler 函数）的性质的研究、积分变换理论的贡献必须在更好的水平上理解. 不幸的是，他的大部分作品都不够受欢迎，因为当时是用俄文出版的。本次调查的目的是填补对 MM Djrbashian 在这些领域的成果的明确认可的空白。出于同样的目的，