Journal ArticleDOI
The rheology of an anelastic medium studied by means of the observation of the splitting of its eigenfrequencies
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In this paper, it is shown how the rheology of anelastic media causes a splitting of each of the free modes of an oscillator into a number of lines spread over a frequency band depending on the type of rheological.Abstract:
It is seen how the rheology of anelastic media causes a splitting of each of the free modes of an oscillator into a number of lines spread over a frequency band depending on the type of rheology. The experimental identification of these lines and/or of the width of each multiplet allows the retrieval of the rheological properties of the medium.read more
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Book ChapterDOI
Multi-index Mittag-Leffler Functions
TL;DR: In this paper, Dzherbashian [Dzh60] defined a function with positive α 1 > 0, α 2 > 0 and real α 1, β 2, β 3, β 4, β 5, β 6, β 7, β 8, β 9, β 10, β 11, β 12, β 13, β 14, β 15, β 16, β 17, β 18, β 20, β 21, β 22, β 24
Journal ArticleDOI
Mean fractional-order-derivatives differential equations and filters
TL;DR: In this paper, the Laplace Transform is used to find the solution of the integro-differential equations defined by means of derivatives of fractional order and their integrals with respect to the order of differentiation.
Journal Article
Time-fractional derivatives in relaxation processes: a tutorial survey
TL;DR: In this article, the basic theory of relaxation processes governed by linear differential equations of fractional order is revisited, and a tutorial survey is provided, with a necessary outline of the classical theory of linear viscoelasticity.
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Time-fractional derivatives in relaxation processes: a tutorial survey
TL;DR: In this paper, the basic theory of relaxation processes governed by linear differential equations of fractional order is revisited, and a tutorial survey is provided, with a necessary outline of the classical theory of linear viscoelasticity.
Journal ArticleDOI
Diffusion with space memory modelled with distributed order space fractional differential equations
TL;DR: Caputo and Plastino as discussed by the authors considered distributed order fractional differential equations in the space domain and introduced the constitutive equation of diffusion in the frequency domain, and obtained the solution of the classic problems with closed form formulae, with the difference with the classic diffusion medium, in the case when a constant boundary pressure is assigned and in the medium the pressure is initially nil.
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