Fractional Differential Equations (eBook)
XII, 146 Seiten
Springer Nature Singapore (Verlag)
978-981-19-7716-9 (ISBN)
The content of the book collects some contributions related to the talks presented during the INdAM Workshop 'Fractional Differential Equations: Modelling, Discretization, and Numerical Solvers', held in Rome, Italy, on July 12-14, 2021. All contributions are original and not published elsewhere.
The main topic of the book is fractional calculus, a topic that addresses the study and application of integrals and derivatives of noninteger order. These operators, unlike the classic operators of integer order, are nonlocal operators and are better suited to describe phenomena with memory (with respect to time and/or space). Although the basic ideas of fractional calculus go back over three centuries, only in recent decades there has been a rapid increase in interest in this field of research due not only to the increasing use of fractional calculus in applications in biology, physics, engineering, probability, etc., but also thanks to the availability of new and more powerful numerical tools that allow for an efficient solution of problems that until a few years ago appeared unsolvable. The analytical solution of fractional differential equations (FDEs) appears even more difficult than in the integer case. Hence, numerical analysis plays a decisive role since practically every type of application of fractional calculus requires adequate numerical tools.
The aim of this book is therefore to collect and spread ideas mainly coming from the two communities of numerical analysts operating in this field - the one working on methods for the solution of differential problems and the one working on the numerical linear algebra side - to share knowledge and create synergies. At the same time, the book intends to realize a direct bridge between researchers working on applications and numerical analysts. Indeed, the book collects papers on applications, numerical methods for differential problems of fractional order, and related aspects in numerical linear algebra.The target audience of the book is scholars interested in recent advancements in fractional calculus.
Angelamaria Cardone is an Associate Professor of Numerical Analysis at the Department of Mathematics, University of Salerno, Italy. Her scientific activity is mainly focused on the numerical solution of Volterra integral equations and of differential equations, also of fractional type, and on the development of related mathematical software.
Marco Donatelli is an Associate Professor of Numerical Analysis at the University of Insubria, Italy. His scientific activity is mainly focused on the regularization of inverse problems and numerical linear algebra methods, with special attention to iterative methods for large linear systems arising from the discretization of integral and differential equations.
Fabio Durastante is a Researcher in Numerical Analysis at the Department of Mathematics, University of Pisa, Italy. His scientific activity is mainly focused on numerical linear algebra and its application to the solution of partial differential equations of both integer and fractional order, high-performance computing, and computation of matrix functions.
Roberto Garrappa is an Associate Professor of Numerical Analysis at the Department of Mathematics, University of Bari, Italy. His scientific activity is mainly focused on numerical methods for fractional differential equations and for the computation of special functions in fractional calculus.
Mariarosa Mazza is a Researcher in Numerical Analysis at the University of Insubria, Italy. Her scientific activity is mainly focused on numerical linear algebra problems and related applications, with special attention to iterative methods for discretized partial differential equations, also of fractional type. Other interests include image deblurring and approximation issues.
Marina Popolizio is an Associate Professor of Numerical Analysis at the Polytechnic University of Bari, Italy. Her scientific activity is mainly focused on numerical linear algebra and numerical methods for fractional differential equations, with special attention to the computation of matrix functions.
The content of the book collects some contributions related to the talks presented during the INdAM Workshop "e;Fractional Differential Equations: Modelling, Discretization, and Numerical Solvers"e;, held in Rome, Italy, on July 12-14, 2021. All contributions are original and not published elsewhere.The main topic of the book is fractional calculus, a topic that addresses the study and application of integrals and derivatives of noninteger order. These operators, unlike the classic operators of integer order, are nonlocal operators and are better suited to describe phenomena with memory (with respect to time and/or space). Although the basic ideas of fractional calculus go back over three centuries, only in recent decades there has been a rapid increase in interest in this field of research due not only to the increasing use of fractional calculus in applications in biology, physics, engineering, probability, etc., but also thanks to the availability of new and more powerful numerical tools that allow for an efficient solution of problems that until a few years ago appeared unsolvable. The analytical solution of fractional differential equations (FDEs) appears even more difficult than in the integer case. Hence, numerical analysis plays a decisive role since practically every type of application of fractional calculus requires adequate numerical tools.The aim of this book is therefore to collect and spread ideas mainly coming from the two communities of numerical analysts operating in this field - the one working on methods for the solution of differential problems and the one working on the numerical linear algebra side - to share knowledge and create synergies. At the same time, the book intends to realize a direct bridge between researchers working on applications and numerical analysts. Indeed, the book collects papers on applications, numerical methods for differential problems of fractional order, and related aspects in numerical linear algebra.The target audience of the book is scholars interested in recent advancements in fractional calculus.
Erscheint lt. Verlag | 16.6.2023 |
---|---|
Reihe/Serie | Springer INdAM Series | Springer INdAM Series |
Zusatzinfo | XII, 146 p. 59 illus., 19 illus. in color. |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Schlagworte | Applications • Computer Science • conference proceedings • Fractional Calculus • fractional differential equations • fractional Laplacian • matrix functions • Mittag-Leffler Function • Non-local methods • Numerical analysis • numerical linear algebra • Research • spectral methods |
ISBN-10 | 981-19-7716-X / 981197716X |
ISBN-13 | 978-981-19-7716-9 / 9789811977169 |
Haben Sie eine Frage zum Produkt? |
![PDF](/img/icon_pdf_big.jpg)
Größe: 6,6 MB
DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.
Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich