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- Title
On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity.
- Authors
Atanackovic, Teodor M.; Djekic, Diana Dolicanin; Gilic, Ersin; Kacapor, Enes
- Abstract
We analyze wave equation for spatially one-dimensional continuum with constitutive equation of non-local type. The deformation is described by a specially selected strain measure with general fractional derivative of the Riesz type. The form of constitutive equation is assumed to be in strain-driven type, often used in nano-mechanics. The resulting equations are solved in the space of tempered distributions by using the Fourier and Laplace transforms. The properties of the solution are examined and compared with the classical case.
- Subjects
ELASTICITY; FRACTIONAL differential equations; FOURIER transforms; WAVE equation; NANOMECHANICS
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 18, p3850
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11183850