Geodesic
Hereditariness and non-locality in wave propagation modelling
Theoretical and applied mechanics, Tome 47 (2020) no. 1.

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The classical wave equation is generalized within the framework of fractional calculus in order to account for the memory and non-local effects that might be material features. Both effects are included in the constitutive equation, while the equation of motion of the deformable body and strain are left unchanged. Memory effects in viscoelastic materials are modeled through the distributed-order fractional constitutive equation that generalizes all linear models having differentiation orders up to order one. The microlocal approach in analyzing singularity propagation is utilized in the case of viscoelastic material described by the fractional Zener model, as well as in the case of two non-local models: non-local Hookean and fractional Eringen.
Keywords: wave equation, memory and non-local effects, distributed-order fractional model, non-local Hookean model, fractional Eringen model 
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     author = {Du\v{s}an Zorica},
     title = {Hereditariness and non-locality in wave propagation modelling},
     journal = {Theoretical and applied mechanics},
     pages = {19 - 31},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2020},
     url = {http://geodesic.mathdoc.fr/item/TAM_2020_47_1_a3/}
}
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Dušan Zorica. Hereditariness and non-locality in wave propagation modelling. Theoretical and applied mechanics, Tome 47 (2020) no. 1. http://geodesic.mathdoc.fr/item/TAM_2020_47_1_a3/