Solution of nonlinear variational problems for generalized fractional viscoelastic models

Solution of nonlinear variational problems for generalized fractional viscoelastic models Full article

Journal

International Journal of Engineering Science
ISSN: 0020-7225

Output data

Year: 2026, Volume: 223, Article number : 104513, Pages count : DOI: 10.1016/j.ijengsci.2026.104513

Tags

Implicit constitutive theory, Volterra integral, Fractional calculus, Variational theory, Mittag-Leffler function

Authors

Hiromichi Itou ¹ , Victor A. Kovtunenko ^2,3 , Masahiro Yamamoto ⁴

Affiliations

1	Department of Mathematics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
2	Department of Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstr.36, 8010 Graz, Austria
3	Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
4	Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

Caputo derivative of fractional order. Constitutive relations of GFV models are given by Volterra hereditary integrals with creep functions described by Prony series replaced with a MittagLeffler function. In a quasi-static situation, the time-dependent equilibrium problem is set in the variational formulation. For linear as well as nonlinear material responses, a solution to the GFV model is provided by an analytical formula of convolution with a solution of the corresponding elastic problem. The numerical example is presented in 1D for a creep test under isotropic expansion, which is analyzed with respect to fractional derivative order and non-linearity.

Hiromichi Itou , Victor A. Kovtunenko , Masahiro Yamamoto
Solution of nonlinear variational problems for generalized fractional viscoelastic models
International Journal of Engineering Science. 2026. V.223. 104513 . DOI: 10.1016/j.ijengsci.2026.104513 WOS Scopus OpenAlex

Submitted:	Dec 9, 2025
Accepted:	Feb 21, 2026

≡ Web of science:	WOS:001709525500001
≡ Scopus:	2-s2.0-105031728911
≡ OpenAlex:	W7133361505