Fractional viscoelastic models for power-law materials
Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad
distribution of time-scales present in their complex internal structure. A promising tool to …
distribution of time-scales present in their complex internal structure. A promising tool to …
An overview of mathematical modelling in cancer research: fractional calculus as modelling tool
LC Vieira, RS Costa, D Valério - Fractal and Fractional, 2023 - mdpi.com
Cancer is a complex disease, responsible for a significant portion of global deaths. The
increasing prioritisation of know-why over know-how approaches in biological research has …
increasing prioritisation of know-why over know-how approaches in biological research has …
[图书][B] Fractional calculus: models and numerical methods
The subject of fractional calculus and its applications (that is, convolution-type pseudo-
differential operators including integrals and derivatives of any arbitrary real or complex …
differential operators including integrals and derivatives of any arbitrary real or complex …
[图书][B] Fractional differential equations and inclusions: classical and advanced topics
S Abbas, M Benchohra, JE Lazreg, JJ Nieto, Y Zhou - 2023 - World Scientific
In this chapter, we introduce notations, definitions, and preliminary facts that will be used in
the remainder of this book. Some notations and definitions from the fractional calculus, some …
the remainder of this book. Some notations and definitions from the fractional calculus, some …
Hybrid Fractional Differential Equations
M Benchohra, E Karapınar, JE Lazreg… - … Differential Equations: New …, 2023 - Springer
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SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …
SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …
How many fractional derivatives are there?
D Valério, MD Ortigueira, AM Lopes - Mathematics, 2022 - mdpi.com
In this paper, we introduce a unified fractional derivative, defined by two parameters (order
and asymmetry). From this, all the interesting derivatives can be obtained. We study the one …
and asymmetry). From this, all the interesting derivatives can be obtained. We study the one …
A comparative study of fractional partial differential equations with the help of yang transform
In applied sciences and engineering, partial differential equations (PDE) of integer and non-
integer order play a crucial role. It can be challenging to determine these equations' exact …
integer order play a crucial role. It can be challenging to determine these equations' exact …
The 21st century systems: An updated vision of continuous-time fractional models
MD Ortigueira, JT Machado - IEEE Circuits and Systems …, 2022 - ieeexplore.ieee.org
This paper presents the continuous-time fractional linear systems and their main properties.
Two particular classes of models are introduced: the fractional autoregressive-moving …
Two particular classes of models are introduced: the fractional autoregressive-moving …
A robust nonlinear PI-type controller for the DC–DC buck–boost power converter
In this study, a novel Lyapunov function-based robust nonlinear proportional–integral (PI)-
type controller for regulating the output voltage of the direct current to direct current (DC–DC) …
type controller for regulating the output voltage of the direct current to direct current (DC–DC) …
A new look at the initial condition problem
MD Ortigueira - Mathematics, 2022 - mdpi.com
In this paper, some myths associated to the initial condition problem are studied and
demystified. It is shown that the initial conditions provided by the one-sided Laplace …
demystified. It is shown that the initial conditions provided by the one-sided Laplace …