The Variable-Order Fractional Calculus of Variations, Almeida
Àâòîð: Almeida Ricardo, Pooseh Shakoor, Torres Delfim F. Íàçâàíèå: Computational Methods in the Fractional Calculus of Variations ISBN: 1783266406 ISBN-13(EAN): 9781783266401 Èçäàòåëüñòâî: World Scientific Publishing Ðåéòèíã: Öåíà: 10296.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: 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.
Àâòîð: Torres Delfim F. M. Íàçâàíèå: Introduction to the Fractional Calculus of Variations ISBN: 1848169663 ISBN-13(EAN): 9781848169661 Èçäàòåëüñòâî: World Scientific Publishing Ðåéòèíã: Öåíà: 10454.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: Suitable for graduate students and ambitious undergraduates in mathematics and mechanics, this title offers an introduction to the subject of Fractional Calculus of Variations (FCV). It describes non-conservative systems in mechanics.
Àâòîð: J. Sabatier; O. P. Agrawal; J. A. Tenreiro Machado Íàçâàíèå: Advances in Fractional Calculus ISBN: 9048175135 ISBN-13(EAN): 9789048175130 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 30039.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing.
Àâòîð: Goodrich, Christopher Peterson, Allan C. Íàçâàíèå: Discrete fractional calculus ISBN: 3319255606 ISBN-13(EAN): 9783319255606 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 6986.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: This text provides the first comprehensive treatment of the discrete fractional calculus. Chapters 1-2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers.
Àâòîð: Agnieszka B. Malinowska; Tatiana Odzijewicz; Delfi Íàçâàíèå: Advanced Methods in the Fractional Calculus of Variations ISBN: 3319147552 ISBN-13(EAN): 9783319147550 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 6986.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå:
1. Introduction.- 2. Fractional Calculus.- 2.1. One-dimensional Fractional Calculus.- 2.2. Multidimensional Fractional Calculus.- 3. Fractional Calculus of Variations.- 3.1. Fractional Euler-Lagrange Equations.- 3.2. Fractional Embedding of Euler-Lagrange Equations.- 4. Standard Methods in Fractional Variational Calculus.- 4.1. Properties of Generalized Fractional Integrals.- 4.2. Fundamental Problem.- 4.3. Free Initial Boundary.- 4.4. Isoperimetric Problem.- 4.5. Noether's Theorem.- 4.6. Variational Calculus in Terms of a Generalized Integral.- 4.7. Generalized Variational Calculus of Several Variables.- 4.8. Conclusion.- 5. Direct Methods in Fractional Calculus of Variations.- 5.1. Existence of a Minimizer for a Generalized Functional.- 5.2. Necessary Optimality Condition for a Minimizer.- 5.3. Some Improvements.- 5.4. Conclusion.- 6. Application to the Sturm-Liouville Problem.- 6.1. Useful Lemmas.- 6.2. The Fractional Sturm-Liouville Problem.- 7. Conclusion.- Appendix - Two Convergence Lemmas.- Index.
Îïèñàíèå: The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.
Àâòîð: Alberto Carpinteri; Francesco Mainardi Íàçâàíèå: Fractals and Fractional Calculus in Continuum Mechanics ISBN: 321182913X ISBN-13(EAN): 9783211829134 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 16979.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.
Îïèñàíèå: Presenting system dynamics as a powerful approach to build simulation models of social systems to aid decision making, this book is grounded in the feedback perspective of complex systems and introduces key concepts such as stocks, flows and feedback. The R programming language provides an open-source and interoperable way to build models.
Àâòîð: Namsrai Khavtgai Íàçâàíèå: Universal Formulas In Integral And Fractional Differential Calculus ISBN: 9814675598 ISBN-13(EAN): 9789814675598 Èçäàòåëüñòâî: World Scientific Publishing Ðåéòèíã: Öåíà: 15048.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: 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.
Àâòîð: Manuel Duarte Ortigueira Íàçâàíèå: Fractional Calculus for Scientists and Engineers ISBN: 9400736371 ISBN-13(EAN): 9789400736375 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 15672.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: In recent years fractional calculus has been rediscovered by scientists and engineers and applied in an increasing number of fields. This book gives a practical and multidisciplinary overview of Fractional Calculus as it relates to Signal Processing.
Àâòîð: Fallahgoul, Hassan Íàçâàíèå: Fractional Calculus and Fractional Processes with Applications to ISBN: 0128042486 ISBN-13(EAN): 9780128042489 Èçäàòåëüñòâî: Elsevier Science Ðåéòèíã: Öåíà: 9264.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå:
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.
