Variational Calculus with Conformable Fractional Derivatives

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.

This is a preprint of a paper whose final and definite form will appear in the IEEE/CAA Journal of Automatica Sinica, ISSN 2329-9266. Submitted 01-Oct-2015; Revised 20-April-2016; Accepted 22-June-2016

References in corpus (8)

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• Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
• Fractional Hamilton formalism within Caputo's derivative
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Cited by in corpus (7)

• A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
• Remarks about the existence of conformable derivatives and some consequences
• A Truly Conformable Calculus on Time Scales
• The solution of conformable Laguerre differential equation using conformable Laplace transform
• Quantization of the Bateman damping system with conformable derivative
• On the Oscillation of Three Dimensional Katugampola Fractional Delay Differential Systems
• About Conformable Derivatives in Banach Spaces