Variable Order Fractional Variational Calculus for Double Integrals by T. Odzijewicz, A. B. Malinowska and D. F. M. Torres
Variable Order Fractional Variational Calculus for Double Integrals - Table of Contents
- PART 1. PRELIMINARIES AND FRACTIONAL OPERATORS
- 1. Introduction and Motivation for Variable Order Operators
- 2. Fractional Integrals and Derivatives of Variable Order
- 3. Properties of Multi-Dimensional Fractional Operators
- 4. Function Spaces and Auxiliary Analytical Tools
- PART 2. DOUBLE INTEGRALS AND VARIATIONAL CALCULUS
- 5. Integration by Parts Formulae for Double Integrals
- 6. Variable Order Fractional Variational Problems
- 7. Euler-Lagrange Equations for Double Integrals
- 8. Transversality and Natural Boundary Conditions
What You Will Learn in Variable Order Fractional Variational Calculus for Double Integrals
Variable Order Fractional Variational Calculus for Double Integrals by Tatiana Odzijewicz, Agnieszka B. Malinowska, and Delfim F. M. Torres is a cutting-edge research monograph that extends classical variational calculus and fixed-order fractional calculus into the advanced domain of variable-order multi-dimensional operators. The text investigates optimization problems governed by double integrals with variable fractional derivatives, covering core advanced topics such as Variable Order Fractional Operators, Integration by Parts Formulae for Multiple Integrals, Fractional Euler-Lagrange Equations, and Natural Boundary Conditions.
This book serves as an invaluable guide for graduate students in applied mathematics, control theorists, and mathematical physicists who want to model complex anomalous diffusion, memory-dependent continuous media, and non-local field phenomena. The authors present rigorous theoretical frameworks supported by systematic mathematical derivations.
Due to its innovative formulation, it is widely recognized as a pioneering reference for modern fractional optimal control and multi-dimensional variational analysis. Rather than focusing solely on single-variable cases, it equips advanced researchers with the analytical tools necessary for advanced physics modeling, non-local mechanics, and advanced calculus of variations.
Book Details & Specifications
Title:
Variable Order Fractional Variational Calculus for Double Integrals by T. Odzijewicz, A. B. Malinowska and D. F. M. Torres
Publisher:
IEEE
Year:
2012
Pages:
6
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
Arxiv License
Amazon:
Amazon
About the Author: Tatiana Odzijewicz
The author Tatiana Odzijewicz
, Agnieszka B. Malinowska, and Delfim F. M. Torres are prominent contemporary mathematicians and leading global experts in the fields of fractional calculus, calculus of variations, and optimal control theory.
Through Variable Order Fractional Variational Calculus for Double Integrals, the authors synthesized advanced non-local operators and multi-dimensional variational principles into a definitive treatise. Their rigorous mathematical expertise makes this text a masterpiece resource for advanced fractional analysis and optimization.
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