On solutions of matrix-valued convolution equations, CM-derivatives and their applications in linear and nonlinear anisotropic viscoelasticity

DOI10.1007/s00033-019-1146-7zbMath1415.74014arXiv2106.07946OpenAlexW2953324161MaRDI QIDQ2421850

Andrzej Hanyga

Publication date: 18 June 2019

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.07946

zbMATH Keywords

viscoelasticityfractional calculuscompletely monotoneStieltjesBernsteinSonine equationcomplete Bernstein

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Linear constitutive equations for materials with memory (74D05)

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Cites Work

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• General fractional calculus, evolution equations, and renewal processes
• Integral equations of the first kind of Sonine type
• Wave propagation in anisotropic viscoelasticity
• Relations between relaxation modulus and creep compliance in anisotropic linear viscoelasticity
• Completely monotonic functions
• Bernstein functions. Theory and applications