On Λ-fractional variational calculus

KA Lazopoulos and AK Lazopoulos*

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. 

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Published on: Mar 1, 2023 Pages: 36-40

Full Text PDF Full Text HTML DOI: 10.17352/amp.000074
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