BOOKS - Fractional Calculus: High-Precision Algorithms and Numerical Implementations
Fractional Calculus: High-Precision Algorithms and Numerical Implementations - Dingyu Xue May 4, 2024 PDF  BOOKS
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Fractional Calculus: High-Precision Algorithms and Numerical Implementations
Author: Dingyu Xue
Year: May 4, 2024
Format: PDF
File size: PDF 6.9 MB
Language: English



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Book Description: Fractional Calculus: High-Precision Algorithms and Numerical Implementations Dingyu Xue May 4, 2024 9789819920693 Synopsis: In an ever-evolving technological landscape, it is crucial to understand the process of technology evolution and its impact on humanity. Fractional calculus and its applications have been a fascinating research area in many engineering disciplines, and this book offers a comprehensive collection of research from one of the most active groups in the field. As the birthplace of one of the four MATLAB toolboxes in fractional calculus, the FOTF Toolbox, this book presents high-precision solution algorithms for various fractional-order differential equations, including nonlinear delay and boundary value equations. Currently, there are no other universal solvers available for these latter two types of equations, making this book an essential resource for readers looking to systematically study the mathematics and solution methods in the field of fractional calculus and apply them to different engineering fields, particularly control systems engineering. The book is a translation of an original German edition, with the help of artificial intelligence machine translation by DeepLcom, followed by a subsequent human revision to ensure stylistic consistency.
Fractional Calculus: High-Precision Algorithms and Numerical Implementations Dingyu Xue May 4, 2024 9789819920693 Synopsis: В постоянно развивающемся технологическом ландшафте крайне важно понимать процесс эволюции технологий и его влияние на человечество. Дробное исчисление и его приложения были увлекательной областью исследований во многих инженерных дисциплинах, и эта книга предлагает исчерпывающую коллекцию исследований одной из самых активных групп в этой области. Являясь родиной одного из четырех наборов инструментов MATLAB в дробном исчислении, FOTF Toolbox, эта книга представляет высокоточные алгоритмы решения для различных дифференциальных уравнений дробного порядка, включая нелинейные уравнения задержки и граничных значений. В настоящее время нет других универсальных решателей, доступных для этих двух последних типов уравнений, что делает эту книгу важным ресурсом для читателей, желающих систематически изучать математику и методы решения в области дробного исчисления и применять их в различных областях техники, в частности, в проектировании систем управления. Книга является переводом оригинального немецкого издания, с помощью машинного перевода DeepLcom, выполненного искусственным интеллектом, с последующей человеческой переработкой для обеспечения стилистической согласованности.
Fractional Calculus: Algorithms de alta precisión e implicaciones numéricas Dingyu Xue May 4, 2024 9789819920693 Synopsis: En un panorama tecnológico en constante evolución, es fundamental comprender el proceso de evolución de la tecnología y su impacto sobre la humanidad. cálculo fraccionado y sus aplicaciones han sido un campo fascinante de investigación en muchas disciplinas de ingeniería, y este libro ofrece una exhaustiva colección de investigación de uno de los grupos más activos en este campo. endo el lugar de nacimiento de uno de los cuatro conjuntos de herramientas MATLAB en el cálculo fraccionario, FOTF Toolbox, este libro presenta algoritmos de solución de alta precisión para diferentes ecuaciones diferenciales de orden fraccionario, incluyendo ecuaciones de latencia no lineal y valores límite. Actualmente no existen otros solucionadores universales disponibles para estos dos últimos tipos de ecuaciones, lo que hace de este libro un recurso importante para los lectores que desean aprender sistemáticamente matemáticas y técnicas de solución en el campo del cálculo fraccionario y aplicarlas en diferentes campos de la técnica, en particular en el diseño de sistemas de control. libro es una traducción de la edición original alemana, mediante la traducción automática de DeepLcom, realizada por inteligencia artificial, con el consiguiente reciclaje humano para garantizar la coherencia estilística.
Fractional Calzus: High-Precision Algorithms and Numerical Influences Dingyu Xue May 4, 2024 9789819920693 Synopsis: In un panorama tecnologico in continua evoluzione, è fondamentale comprendere l'evoluzione della tecnologia e il suo impatto sull'umanità. Il calcolo frazionale e le sue applicazioni sono stati un campo di ricerca affascinante in molte discipline di ingegneria, e questo libro offre una raccolta completa di studi di uno dei gruppi più attivi in questo campo. Essendo la patria di uno dei quattro set di strumenti MATLAB in frazionamento, FOTF Toolbox, questo libro presenta algoritmi di precisione per diverse equazioni differenziali di ordine frazionario, comprese le relazioni di ritardo non lineare e i valori limite. Al momento non ci sono altri risolutori universali disponibili per questi ultimi due tipi di equazioni, il che rende questo libro una risorsa importante per i lettori che desiderano studiare sistematicamente matematica e metodi di soluzione in termini di calcolo frazionale e applicarli in diverse aree tecniche, in particolare nella progettazione di sistemi di gestione. Il libro è una traduzione della pubblicazione originale tedesca, attraverso la traduzione automatica di un DeepLcom realizzato dall'intelligenza artificiale, con la successiva trasformazione umana per garantire la coerenza stilistica.
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Fractional Calculus:高精度アルゴリズムと数値実装Dingyu Xue May 4、 2024 9789819920693 Synopsis:進化を続ける技術風景の中で、テクノロジーの進化とその人類への影響を理解することが重要です。フラクショナル微積分とその応用は、多くの工学分野で魅力的な研究分野であり、この本は、分野で最も活発なグループの1つによる研究の包括的なコレクションを提供しています。MATLABツール、FOTFツールボックスの4つのフラクショナル計算のうちの1つである本書では、非線形遅延や境界値方程式を含む様々なフラクショナルオーダー微分方程式の高精度なソリューションアルゴリズムを紹介しています。現在、これらの2種類の方程式には他にユニバーサルソルバーが存在しないため、この本は、数学や分数計算の分野での解法を体系的に研究し、それらを工学の様々な分野、特に制御システムの設計に適用したい読者にとって重要なリソースとなっています。本書は、DeepLcomの人工知能機械翻訳を使用したオリジナルのドイツ語版の翻訳であり、文体の一貫性を確保するために人間の改訂が続きます。

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