Advanced methods in the fractional calculus of variations:
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ADVANCED METHODS IN THE FRACTIONAL CALCULUS OF VARIATIONS
/ MALINOWSKA, AGNIESZKA B.
: 2015
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
ADVANCED METHODS IN THE FRACTIONAL CALCULUS OF VARIATIONS
/ MALINOWSKA, AGNIESZKA B.
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
1. INTRODUCTION
2. FRACTIONAL CALCULUS
3. FRACTIONAL CALCULUS OF VARIATIONS
4. STANDARD METHODS IN FRACTIONAL VARIATIONAL CALCULUS
5. DIRECT METHODS IN FRACTIONAL CALCULUS OF VARIATIONS
6. APPLICATION TO THE STURM-LIOUVILLE PROBLEM
7. CONCLUSION
APPENDIX - TWO CONVERGENCE LEMMAS
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. |
| any_adam_object | 1 |
| author | Malinowska, Agnieszka B. Odzijewicz, Tatiana Torres, Delfim F. M. 1971- |
| author_GND | (DE-588)1029177791 (DE-588)1069005045 (DE-588)1029177880 |
| author_facet | Malinowska, Agnieszka B. Odzijewicz, Tatiana Torres, Delfim F. M. 1971- |
| author_role | aut aut aut |
| author_sort | Malinowska, Agnieszka B. |
| author_variant | a b m ab abm t o to d f m t dfm dfmt |
| building | Verbundindex |
| bvnumber | BV042387174 |
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| dewey-full | 515.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.64 |
| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-14756-7 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2025-03-03T05:00:10Z |
| institution | BVB |
| isbn | 9783319147567 |
| issn | 2191-530X |
| language | English |
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| spellingShingle | Malinowska, Agnieszka B. Odzijewicz, Tatiana Torres, Delfim F. M. 1971- Advanced methods in the fractional calculus of variations Mathematics Systems theory Mathematical optimization Mathematical physics Economics, Mathematical Calculus of Variations and Optimal Control; Optimization Control Mathematical Methods in Physics Game Theory/Mathematical Methods Mathematical Modeling and Industrial Mathematics Systems Theory, Control Mathematik Mathematische Physik |
| title | Advanced methods in the fractional calculus of variations |
| title_auth | Advanced methods in the fractional calculus of variations |
| title_exact_search | Advanced methods in the fractional calculus of variations |
| title_full | Advanced methods in the fractional calculus of variations Agnieszka B. Malinowska ; Tatiana Odzijewicz ; Delfim F. M. Torres |
| title_fullStr | Advanced methods in the fractional calculus of variations Agnieszka B. Malinowska ; Tatiana Odzijewicz ; Delfim F. M. Torres |
| title_full_unstemmed | Advanced methods in the fractional calculus of variations Agnieszka B. Malinowska ; Tatiana Odzijewicz ; Delfim F. M. Torres |
| title_short | Advanced methods in the fractional calculus of variations |
| title_sort | advanced methods in the fractional calculus of variations |
| topic | Mathematics Systems theory Mathematical optimization Mathematical physics Economics, Mathematical Calculus of Variations and Optimal Control; Optimization Control Mathematical Methods in Physics Game Theory/Mathematical Methods Mathematical Modeling and Industrial Mathematics Systems Theory, Control Mathematik Mathematische Physik |
| topic_facet | Mathematics Systems theory Mathematical optimization Mathematical physics Economics, Mathematical Calculus of Variations and Optimal Control; Optimization Control Mathematical Methods in Physics Game Theory/Mathematical Methods Mathematical Modeling and Industrial Mathematics Systems Theory, Control Mathematik Mathematische Physik |
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