Storage and dissipation of energy in Prabhakar viscoelasticity

DOI10.3390/MATH6020015zbMath1454.74024arXiv1712.09419OpenAlexW2780402795MaRDI QIDQ1657259

Ivano Colombaro, Andrea Giusti, Silvia Vitali

Publication date: 13 August 2018

Published in: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09419

zbMATH Keywords

Mittag-Leffler functionintegral transformfractional calculusseismology

Mathematics Subject Classification ID

Seismology (including tsunami modeling), earthquakes (86A15) Fractional derivatives and integrals (26A33) Linear constitutive equations for materials with memory (74D05) Geophysical solid mechanics (74L05)

Related Items (15)

Solving Prabhakar differential equations using Mikusiński's operational calculus ⋮ Mikusiński's operational calculus for Prabhakar fractional calculus ⋮ Computing the matrix Mittag-Leffler function with applications to fractional calculus ⋮ Editorial. Fractional calculus: theory and applications ⋮ A practical guide to Prabhakar fractional calculus ⋮ A catalogue of semigroup properties for integral operators with Fox–Wright kernel functions ⋮ Energy dissipation in viscoelastic Bessel media ⋮ Stability of fractional-order systems with Prabhakar derivatives ⋮ An operational calculus approach to Hilfer-Prabhakar fractional derivatives ⋮ General fractional calculus and Prabhakar's theory ⋮ Nonlocal effects on the dynamic analysis of a viscoelastic nanobeam using a fractional Zener model ⋮ A comment on some new definitions of fractional derivative ⋮ Response functions in linear viscoelastic constitutive equations and related fractional operators ⋮ A system of Cauchy fractional differential equations and new properties of Mittag-Leffler functions with matrix argument ⋮ Existence results for a generalization of the time-fractional diffusion equation with variable coefficients

Uses Software

• ML

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hilfer-Prabhakar derivatives and some applications
• A dynamic viscoelastic analogy for fluid-filled elastic tubes
• On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics
• On a mathematical framework for the constitutive equations of anisotropic dielectric relaxation
• Fractals and fractional calculus in continuum mechanics
• Generalized Langevin equation and the Prabhakar derivative
• Wave propagation in linear viscoelastic media with completely monotonic relaxation moduli
• A comment on some new definitions of fractional derivative
• Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models
• Prabhakar-like fractional viscoelasticity
• The Prabhakar or three parameter Mittag-Leffler function: theory and application
• A class of linear viscoelastic models based on Bessel functions
• Models of dielectric relaxation based on completely monotone functions
• On infinite order differential operators in fractional viscoelasticity
• On the propagation of transient waves in a viscoelastic Bessel medium
• From Bessel to Multi-Index Mittag–Leffler Functions
• Viscoelastic Waves in Layered Media
• Fractional Diffusion--Telegraph Equations and Their Associated Stochastic Solutions
• Relaxation, dispersion, attenuation, and finite propagation speed in viscoelastic media
• Mittag-Leffler Functions, Related Topics and Applications

This page was built for publication: Storage and dissipation of energy in Prabhakar viscoelasticity