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Geometrical enhancement of the electric field: Application of fractional calculus in nanoplasmonics

, 2011
We developed an analytical approach, for a wave propagation in metal-dielectric nanostructures in the quasi-static limit. This consideration establishes a link between fractional geometry of the nanostructure and fractional integro-differentiation.
Baskin, E., Iomin, A.
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Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics

, 2011
Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics.
Dumitru Baleanu +3 more
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Covariance in fractional calculus

International Journal of Modern Physics A
Based on the requirement of covariance, we propose a new approach for generalizing fractional calculus in multi-dimensional space. As a first application, we calculate an approximation for the ground state energy of the fractional two-dimensional harmonic oscillator using the Ritz variational principle.
openaire +2 more sources

Numerical Approximations to Fractional Problems of the Calculus of Variations and Optimal Control

, 2013
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating the ...
Almeida, Ricardo, Pooseh, Shakoor, Torres, Delfim F. M. +2 more
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Fractional calculus and the evolution of fractal phenomena [PDF]

, 1999
Andrea Rocco, Bruce J. West
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The Memory Effect on Fractional Calculus: An Application in the Spread of Covid-19 [PDF]