Variational Calculus With Conformable Fractional Derivatives

Matheus J. Lazo; DelfimF.M. Torres

doi:10.1109/JAS.2016.7510160

Volume 4 Issue 2

Apr. 2017

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2017 > 4(2): 340-352

Matheus J. Lazo and DelfimF.M. Torres, "Variational Calculus With Conformable Fractional Derivatives," IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 340-352, Apr. 2017. doi: 10.1109/JAS.2016.7510160

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Matheus J. Lazo and DelfimF.M. Torres, "Variational Calculus With Conformable Fractional Derivatives," IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 340-352, Apr. 2017. doi: 10.1109/JAS.2016.7510160

Matheus J. Lazo and DelfimF.M. Torres, "Variational Calculus With Conformable Fractional Derivatives," IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 340-352, Apr. 2017. doi: 10.1109/JAS.2016.7510160

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Variational Calculus With Conformable Fractional Derivatives

doi: 10.1109/JAS.2016.7510160

Matheus J. Lazo^1
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DelfimF.M. Torres^{2
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1.
Instituto de Matemática, Estatística e Física-FURG, Rio Grande, RS 96.201-900, Brazil
2.
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro 3810-193, Portugal

Funds: This work was partially supported by CNPq and CAPES (Brazilian research funding agencies), and Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA), and also the Portuguese Foundation for Science and Technology (FCT), within project UID/MAT/04106/2013

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Abstract

Abstract

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.
- Conformable fractional derivative,
- fractional calculus of variations,
- fractional optimal control,
- invariant variational conditions,
- Noether's theorem

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References

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Variational Calculus With Conformable Fractional Derivatives

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