New rheological problems involving general fractional derivatives with nonsingular power-law kernels

Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science

Xiao-Jun YANG¹ 

关键词: general fractional derivatives with nonsingular power-law kernel;    general fractional-order;    Voigt model;    general fractional-order Maxwell model;    Laplace transform;    rheology.;   

DOI  :  

学科分类：计算机科学（综合）

来源: Editura Academiei Romane

【 摘 要 】

In this paper we propose the general Riemann-Liouville and Caputo-Liouville fractionalderivatives with nonsingular power-law kernels, for the first time to our knowledge. New general lawsof deformation within the framework of the general fractional derivatives are considered in detail. Thecreep and relaxation behaviors of the general fractional-order Voigt and Maxwell models are alsoobtained with the use of the Laplace transform. We provide the mathematical tools to describe therheological phenomena of real materials with the memory effect.

【 授权许可】

Unknown