Reflections on two parallel ways in the progress of fractional calculus in mechanics of solids

YA Rossikhin - 2010 - asmedigitalcollection.asme.org
Interest in fractional calculus has quickened profoundly in the past few decades, resulting in
a large body of articles devoted to this challenge, and sometimes researchers, especially …

[KNIHA][B] Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models

F Mainardi - 2022 - books.google.com
Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained
treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation …

Analysis of fractional differential equations

K Diethelm, NJ Ford - Journal of Mathematical Analysis and Applications, 2002 - Elsevier
We discuss existence, uniqueness, and structural stability of solutions of nonlinear
differential equations of fractional order. The differential operators are taken in the Riemann …

Fractional modeling of blood ethanol concentration system with real data application

S Qureshi, A Yusuf, AA Shaikh, M Inc… - … Journal of Nonlinear …, 2019 - pubs.aip.org
In this study, a physical system called the blood ethanol concentration model has been
investigated in its fractional (non-integer) order version. The three most commonly used …

Fractional-order circuits and systems: An emerging interdisciplinary research area

AS Elwakil - IEEE Circuits and Systems Magazine, 2010 - ieeexplore.ieee.org
A recent article published in this magazine has labeled fractional-order continuous-time
systems as the" 21st century systems". Indeed, this emerging research area is slowly gaining …

A method based on the Jacobi tau approximation for solving multi-term time–space fractional partial differential equations

AH Bhrawy, MA Zaky - Journal of Computational Physics, 2015 - Elsevier
In this paper, we propose and analyze an efficient operational formulation of spectral tau
method for multi-term time–space fractional differential equation with Dirichlet boundary …

Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations

V Taç, MK Rausch, FS Costabal, AB Tepole - Computer methods in applied …, 2023 - Elsevier
We develop a fully data-driven model of anisotropic finite viscoelasticity using neural
ordinary differential equations as building blocks. We replace the Helmholtz free energy …

[PDF][PDF] The analysis of fractional differential equations

K Diethelm, NJ Ford - Lecture notes in mathematics, 2010 - academia.edu
Analysis of Fractional Differential Equations Page 1 See discussions, stats, and author profiles
for this publication at: https://www.researchgate.net/publication/222299516 Analysis of …

[KNIHA][B] Метод дробных производных

ВВ Учайкин - 2008 - elibrary.ru
Книга содержит изложение метода дробных производных и состоит из трех частей,
раскрывающих физические основания метода, математический аппарат и примеры …

A survey of single and multi-component Fractional-Order Elements (FOEs) and their applications

ZM Shah, MY Kathjoo, FA Khanday, K Biswas… - Microelectronics …, 2019 - Elsevier
Fractional-Order circuits and networks being a widely researched field lags in its
development due to the non-availability of its basic building block ie Fractional-Order …