Fractional Calculus in Analysis, Dynamics & Optimal Control (Hardcover)

Jacky Cresson

ISBN 10: 1629486353 / ISBN 13: 9781629486352

Editore: Nova Science Publishers Inc, New York, 2014

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Hardcover. This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for classical dissipative partial differential equations. In continuation of this chapter, a fractional analogue of the classical Pontryagin maximum principle is proved for discrete and continuous fractional optimal control problems. The fourth chapter gives a first mathematical model that allows a rigorous connection to be made between the dynamics of chaotic Hamiltonian systems and fractional dynamics, mixing the previous approaches of G Zaslavsky and R Hilfer. Finally, numerical methods to deal with fractional optimal control problems are discussed and implemented. All the chapters are self-contained and complete proofs are given. This text is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9781629486352

Dati bibliografici

• Titolo: Fractional Calculus in Analysis, Dynamics & Optimal Control (Hardcover)
• Editore: Nova Science Publishers Inc, New York
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 1629486353
• ISBN 13: 9781629486352
• Rilegatura: Hardcover
• Condizione: new

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Riassunto

This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for classical dissipative partial differential equations. In continuation of this chapter, a fractional analogue of the classical Pontryagin maximum principle is proved for discrete and continuous fractional optimal control problems. The fourth chapter gives a first mathematical model that allows a rigorous connection to be made between the dynamics of chaotic Hamiltonian systems and fractional dynamics, mixing the previous approaches of G Zaslavsky and R Hilfer. Finally, numerical methods to deal with fractional optimal control problems are discussed and implemented. All the chapters are self-contained and complete proofs are given.