On Λ-fractional variational calculus
<p>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 accepte...
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| Main Authors: | , |
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| Format: | Book |
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Annals of Mathematics and Physics - Peertechz Publications,
2023-03-01.
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| Online Access: | Connect to this object online. |
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| Summary: | <p>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. </p> |
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| DOI: | 10.17352/amp.000074 |