Computational Methods in the Fractional Calculus of Variations

This book fills a gap in the literature by introducing numerical techniques to solve problems of 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.

The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.

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Contents:IntroductionThe Calculus of Variations and Optimal ControlFractional CalculusFractional Variational ProblemsNumerical Methods for Fractional Variational ProblemsApproximating Fractional DerivativesApproximating Fractional IntegralsDirect MethodsIndirect MethodsFractional Optimal Control with Free End-PointsAn Expansion Formula for Fractional Operators of Variable OrderDiscrete-Time Fractional Calculus of VariationsConclusion
Readership: Advanced undergraduate, graduate students and researchers in mathematics, physics and applied sciences.
Key Features:Deals with an important subject, which has gained traction in the last two decadesNo other book deals with computational methods in fractional calculus of variationsServes as a good complement to A B Malinowska and D F M Torres, Introduction to the Fractional Calculus of Variations, Imperial College Press, London, 2012. That book whereas deals with the mathematical foundations of fractional variational calculus, this book is devoted to the computational aspects of the subject