[图书][B] General fractional derivatives: theory, methods and applications

XJ Yang - 2019 - taylorfrancis.com
General Fractional Derivatives: Theory, Methods and Applications provides knowledge of
the special functions with respect to another function, and the integro-differential operators …

[图书][B] Mittag-Leffler functions, related topics and applications

R Gorenflo, AA Kilbas, F Mainardi, SV Rogosin - 2020 - Springer
Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

[图书][B] General fractional derivatives with applications in viscoelasticity

XJ Yang, F Gao, Y Ju - 2020 - books.google.com
General Fractional Derivatives with Applications in Viscoelasticity introduces the newly
established fractional-order calculus operators involving singular and non-singular kernels …

Leibniz type rule: ψ-Hilfer fractional operator

JVC Sousa, EC De Oliveira - Communications in Nonlinear Science and …, 2019 - Elsevier
In this paper, we present a Leibniz type rule for the ψ-Hilfer (ψ-H) fractional derivative
operator in two forms, one written in terms of the ψ-Riemann-Liouville (ψ-RL) fractional …

A triaxial creep model for salt rocks based on variable-order fractional derivative

W Fei, L Jie, Z Quanle, L Cunbao, C Jie… - Mechanics of Time …, 2021 - Springer
This paper intend to describe the entire creep process of a salt rock under triaxial loading,
especially the creep characteristics in the accelerated creep stage, by replacing the …

Modeling biological systems with an improved fractional Gompertz law

L Frunzo, R Garra, A Giusti, V Luongo - Communications in Nonlinear …, 2019 - Elsevier
The aim of this paper is to provide a fractional generalization of the Gompertz law via a
Caputo-like definition of fractional derivative of a function with respect to another function. In …

A novel approach to nonlinear variable-order fractional viscoelasticity

M Di Paola, G Alotta, A Burlon… - … Transactions of the …, 2020 - royalsocietypublishing.org
This paper addresses nonlinear viscoelastic behaviour of fractional systems with variable
time-dependent fractional order. In this case, the main challenge is that the Boltzmann linear …

A variable-order fractional derivative creep constitutive model of salt rock based on the damage effect

J Liu, F Wu, Q Zou, J Chen, S Ren, C Zhang - … and geophysics for geo …, 2021 - Springer
The rheological properties of rock are the main factors affecting the long-term stability of
geotechnical engineering. However, the nonlinear rheological behavior in accelerating …

A unified Maxwell model with time-varying viscosity via ψ-Caputo fractional derivative coined

J Li, L Ma - Chaos, Solitons & Fractals, 2023 - Elsevier
In order to describe the mechanical behaviors of viscoelastic materials that couple memory
effects and time-varying viscosity properties toggled between thixotropy and rheopexy, this …

Developing a two-step improved damage creep constitutive model based on soft rock saturation-loss cycle triaxial creep test

A Li, H Deng, H Zhang, M Jiang, H Liu, Y Xiao, J Wen - Natural Hazards, 2021 - Springer
The study of the time-dependent deformation behavior of soft rock under water–rock
interaction is of great significance to reveal slope creep deformation behavior. In this study …