Agnieszka B. Malinowska's Books

Quantum Variational Calculus

By: Agnieszka B. Malinowska,Delfim F.M. Torres

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Quantum Variational Calculus

By: Agnieszka B. Malinowska,Delfim F.M. Torres

This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.

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Springer Science & Business Media

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ISBN 10

3319027476

ISBN 13

9783319027470

Advanced Methods in the Fractional Calculus of Variations

By: Agnieszka B. Malinowska,Tatiana Odzijewicz,Delfim F.M. Torres

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Advanced Methods in the Fractional Calculus of Variations

By: Agnieszka B. Malinowska,Tatiana Odzijewicz,Delfim F.M. Torres

This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm–Liouville problems. Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.

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142

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Springer

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ISBN 10

3319147560

ISBN 13

9783319147567

Introduction To The Fractional Calculus Of Variations

By: Delfim F M Torres,Agnieszka Barbara Malinowska

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Introduction To The Fractional Calculus Of Variations

By: Delfim F M Torres,Agnieszka Barbara Malinowska

This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler-Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature./a

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Page Count

292

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

184816968X

ISBN 13

9781848169685

Book's by Agnieszka B. Malinowska

Quantum Variational Calculus

Quantum Variational Calculus

Advanced Methods in the Fractional Calculus of Variations

Advanced Methods in the Fractional Calculus of Variations

Introduction To The Fractional Calculus Of Variations

Introduction To The Fractional Calculus Of Variations

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