英文专著《FRACTIONAL INTEGRALS AND DERIVATIVES: Theory and Applications》的翻译

Fractional integrals and derivatives are effective tools to describe historical dependence and spatial global correlation. From the references available, they have potential applications in the scientific disciplines such as physics, biology, engineering so as to attract the wide attention and interest of scientists and engineers. At present, more and more scholars from mathematics, physics, biology, mechanics and control have joined the research upsurge in China, but there is a lack of a comprehensive, systematic and in-depth Chinese reference book of fractional calculus. Former Soviet scholars Stefan G. Samko, Anatoly A. Kilbas, and Oleg I. Marichev had their monograph “FRACTIONAL INTEGRALS AND DERIVATIVES: Theory and Applications” published in Gordon and Breach Science Publishers which covers over 1000 pages, but it has not been published yet due to copyright. In view of the urgent need of domestic scholars, the applicant intends to translate the above monograph into Chinese and present it to the readers, so as to promote the development of fractional calculus theory and its applications in China.

分数阶积分和导数是描述历史依赖性和空间全域相关性的有效工具。从现有文献来看，它们在物理、生物、工程等领域有着潜在的应用，从而引起科学家和工程师的广泛关注和兴趣。目前，国内已有越来越多的来自数学、物理、生物、力学、控制等领域的学者加入到这一研究热潮之中，但缺少一本全面、系统、深入的分数阶微积分的中文参考书。虽然前苏联学者Stefan G. Samko、Anatoly A. Kilbas、Oleg I. Marichev在Gordon and Breach Science Publishers出版了1000余页的专著《FRACTIONAL INTEGRALS AND DERIVATIVES: Theory and Applications》, 但由于版权原因该出版社已不再出版此专著了。鉴于国内学者的迫切需要，申请人拟将上述专著翻译成中文呈现在读者面前，促进分数阶微积分理论和应用在中国的发展。

分数阶微积分与整数阶微积分不同，它总是先介绍分数阶积分，然后再介绍分数阶导数。现已发现，分数阶积分和导数是描述历史依赖性和空间全域相关性的有效工具，它们在物理、工程等领域有着潜在的应用，从而引起众多科学家和工程师的广泛关注和兴趣。目前，国内已有越来越多的来自数学、力学、控制等领域的学者加入到这一研究热潮之中，但缺少一本全面、系统、深入的分数阶微积分的中文参考书。前苏联学者Samko、Kilbas、Marichev在Gordon and Breach Science Publishers出版了近1000页的专著《FRACTIONAL INTEGRALS AND DERIVATIVES: Theory and Applications》，由于版权原因已不再出版了。鉴于国内学者的迫切需要，申请人将上述专著翻译成中文呈现在读者面前，促进分数阶微积分理论和应用在中国的发展。. 翻译此专著是申请人在其研究小组上讲授的基础上进行的，经过2022年这一年的努力，中文初稿已经完成。接下来进行仔细校对，然后寄送给同行，希望学术同行提意见，2023年下半年交付给科学出版社出版。