Constrained Fractional Variational Problems of Variable Order

Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint.In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of variable fractional order and we present a new variational pro...

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Bibliographic Details
Published inIEEE/CAA journal of automatica sinica Vol. 4; no. 1; pp. 80 - 88
Main Authors Tavares, Dina, Almeida, Ricardo, Torres, Delfim F. M.
Format Journal Article
LanguageEnglish
Published Piscataway Chinese Association of Automation (CAA) 01.01.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Boundary conditions
Constraints
Derivatives
Differential equations
Electronic mail
Fractional calculus
Integral equations
Integrals
Isoperimetric problem
Optimization
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Summary:Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint.In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of variable fractional order and we present a new variational problem subject to a holonomic constraint. We establish necessary optimality conditions in order to determine the minimizers of the fractional problems. The terminal point in the cost integral,as well as the terminal state, are considered to be free, and we obtain corresponding natural boundary conditions.
Bibliography:Dina Tavares;Ricardo Almeida;Delfim F.M.Torres;Department of Mathematics, Polytechnic Institute of Leiria;Department of Mathematics, University of Aveiro
10-1193/TP
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2329-9266
2329-9274
DOI:10.1109/JAS.2017.7510331