Study on the performance of variable-order fractional viscoelastic models to the order function parameters

Meng, Runquan; Cao, Liu; Zhang, Qindan

doi:10.1016/j.apm.2023.05.017

Cited by 14 publications

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The theory and applications of fractional calculus have grabbed increasing attention [1–10] due to the advantage of fractional calculus in characterizing the hereditary properties of various materials and processes. And recently, the variable order fractional calculus was presented and developed to describe more complex phenomena in various fields of science and engineering [11–17].…”

Section: Introductionmentioning

confidence: 99%

Impulsive fractional partial differential system and its correct equivalent integral equation

Zhang,

Liu,

Peng

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

It is found that there are two piecewise functions to satisfy the conditions in the impulsive fractional partial differential system (IFrPDS), which deduce that the three different equivalent integral equations of the IFrPDS given in the cited papers are inappropriate. Next, by applying two limit properties of the IFrPDS and the properties of piecewise function, the new formula of equivalent integral equation of the IFrPDS is discovered that is the integral equation with an arbitrary continuously differentiable function of on to reveal the non‐uniqueness of the IFrPDE's solution. Finally, an example is provided to expound the computation of the equivalent integral equation of the IFrPDS.

show abstract

Section: Introductionmentioning

confidence: 99%

Impulsive fractional partial differential system and its correct equivalent integral equation

Zhang,

Liu,

Peng

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

On variable-order fractional linear viscoelasticity

Giusti,

Colombaro,

Garra

et al. 2024

Fract Calc Appl Anal

View full text Add to dashboard Cite

A generalization of fractional linear viscoelasticity based on Scarpi’s approach to variable-order fractional calculus is presented. After reviewing the general mathematical framework, a variable-order fractional Maxwell model is analysed as a prototypical example for the theory. Some physical considerations are then provided concerning the fractionalisation procedure and the choice of the transition functions. Lastly, the material functions for the considered model are derived and numerically evaluated for exponential-type and Mittag-Leffler-type order functions.

show abstract

Reduced-Order Observer-Based Event-Triggered Adaptive Fuzzy Backstepping Control of Uncertain Fractional-Order Strict Feedback Nonlinear Systems

Yang,

2024

Int. J. Fuzzy Syst.

View full text Add to dashboard Cite

Study on the performance of variable-order fractional viscoelastic models to the order function parameters

Cited by 14 publications

References 23 publications

Impulsive fractional partial differential system and its correct equivalent integral equation

Impulsive fractional partial differential system and its correct equivalent integral equation

On variable-order fractional linear viscoelasticity

Reduced-Order Observer-Based Event-Triggered Adaptive Fuzzy Backstepping Control of Uncertain Fractional-Order Strict Feedback Nonlinear Systems

Contact Info

Product

Resources

About