Introduction to the Fractional Calculus of Variations, Torres Delfim F. M.

Автор: Fallahgoul, Hassan
Название: Fractional Calculus and Fractional Processes with Applications to
ISBN: 0128042486 ISBN-13(EAN): 9780128042489
Издательство: Elsevier Science
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Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization.

Автор: Baleanu Dumitru, Diethelm Kai, Scalas Enrico
Название: Fractional Calculus: Models and Numerical Methods (Second Edition)
ISBN: 9813140038 ISBN-13(EAN): 9789813140035
Издательство: World Scientific Publishing
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Описание: This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.

Автор: Podlubny, Igor.
Название: Fractional differential equations :
ISBN: 0125588402 ISBN-13(EAN): 9780125588409
Издательство: Elsevier Science
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Описание: Intended for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, this covers the topics necessary for initial study and immediate application of fractional derivatives fractional differential equations. It also includes tables of fractional derivatives.

Автор: Namsrai Khavtgai
Название: Universal Formulas In Integral And Fractional Differential Calculus
ISBN: 9814675598 ISBN-13(EAN): 9789814675598
Издательство: World Scientific Publishing
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Описание: This table-top reference book presents unique and traditional analytic calculations, and features more than a hundred universal formulas where one can calculate by hand enormous numbers of definite integrals, fractional derivatives and inverse operators.

Автор: Almeida Ricardo, Pooseh Shakoor, Torres Delfim F.
Название: Computational Methods in the Fractional Calculus of Variations
ISBN: 1783266406 ISBN-13(EAN): 9781783266401
Издательство: World Scientific Publishing
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Описание: This book fills a gap in the literature by introducing numerical techniques to solve problems of the Fractional Calculus of Variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.