Abstract Editorial Note: This is a paper by M.M. Djrbashian and A.B. Nersesian of 1968, that was published in Russian. There is a constant interest to Djrbashian’s contributions to the topic of fractional calculus and theory of Mittag-Leffler function. Unfortunately, his works were published in Russian and thus, are not easy accessible and not enough popular. Therefore, we invited hS. Rogosin and M. Dubatovskaya to prepare the survey paper in this same issue of “FCAA” and also to translate and edit the present paper in English. On behalf of Editorial Board and fractional calculus’ community, we express to them our thanks for this hard work, including also retyping, mentioning some typos, etc. Authors’ Summary: The concept of fractional integro-differentiation has found a number of applications in earlier papers of the present authors. With this paper we begin the publication of our results in the field of boundary problems for differential operators of fractional order.

中文翻译：

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分数阶微分方程的分数阶导数和柯西问题

摘要 编者按：这是MM Djrbashian 和AB Nersesian 于1968 年发表的论文，以俄文发表。Djrbashian 对分数阶微积分和 Mittag-Leffler 函数理论的贡献一直受到关注。不幸的是，他的作品是用俄语出版的，因此不容易获得，也不够受欢迎。因此，我们邀请了hS。Rogosin 和 M. Dubatovskaya 准备了同一期“FCAA”的调查论文，并用英文翻译和编辑本论文。我们代表编委会和分数阶微积分社区，向他们的辛勤工作表示感谢，包括重新打字，提到一些错别字等。 作者总结：分数积分微分的概念在许多领域得到了应用。本作者的早期论文。