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Volume 4 Issue 1
Jan.  2017

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2017  >  4(1): 80-88
Dina Tavares, Ricardo Almeida and Delfim F. M. Torres, "Constrained Fractional Variational Problems of Variable Order," IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 80-88, Jan. 2017. doi: 10.1109/JAS.2017.7510331
Citation: Dina Tavares, Ricardo Almeida and Delfim F. M. Torres, "Constrained Fractional Variational Problems of Variable Order," IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 80-88, Jan. 2017. doi: 10.1109/JAS.2017.7510331
shu

Constrained Fractional Variational Problems of Variable Order

doi: 10.1109/JAS.2017.7510331
  • 1.

    Department of Mathematics, Polytechnic Institute of Leiria, 2410-272 Leiria, Portugal

  • 2.

    Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Funds:  This work was supported by Portuguese Funds through the Center for Research and Development in Mathematics and Applications (CIDMA) and the Portuguese Foundation for Science and Technology (FCT) (UID/MAT/04106/2013). Tavares was also supported by FCT through the Ph.D. fellowship SFRH/BD/42557/2007
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    Abstract
  • 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.

     

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