On Λ-fractional variational calculus
- 1 March 2023
- journal article
- Published by Peertechz Publications Private Limited in Annals of Mathematics and Physics
- Vol. 6 (1), 036-040
- https://doi.org/10.17352/amp.000074
Abstract
Pointing out that Λ-fractional analysis is the unique fractional calculus theory including mathematically acceptable fractional derivatives, variational calculus for Λ-fractional analysis is established. Since Λ-fractional analysis is a non-local procedure, global extremals are only accepted. That means the extremals should satisfy not only the Euler–Lagrange equation but also the additional Weierstrass-Erdmann corner conditions. Hence non-local stability criteria are introduced. The proposed variational procedure is applied to any branch of physics, mechanics, biomechanics, etc. The present analysis is applied to the Λ-fractional refraction of light.Keywords
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