Non-local continuum mechanics and fractional calculus

By K. A. Lazopoulos. 2006

202 citations recorded by the source corpus.

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Long-range cohesive interactions of non-local continuum faced by fractional calculus (2008, background): “(4) has been formulated (Lazopoulos, 2006) under the assumptions of vanishing boundary condition of the model as u(0) = u(L) = 0.”
Fractional order constitutive model of geomaterials under the condition of triaxial test (2013, background): “Padovan[11] and others[12-18] have examined various issues involved in the numerical implementation of these sorts of models.”
A Fractional Model of Continuum Mechanics (2012, background): “More recently, it has been shown that fractional calculus can be related to new non-local constitutive laws of elasticity [13, 14, 17, 18, 32, 52] as well as to the mechanics of fractal media [9–11].”
Variational problems with fractional derivatives: Euler–Lagrange equations (2008, methodology): “applied the fractional Euler-Lagrange equations to examine fractional Lagrangian and Hamiltonian systems linear in velocities. Other applications of fractional variational principles are presented in [4, 5, 6, 9, 10, 12, 23, 24, 26, 27, 29]. We cite here also the work of G. S. F. Frederico and D. F.”