Related papers: An Efficient and Accurate Method for Modeling Nonl…
A fractional derivative is a temporally nonlocal operation which is computationally intensive due to inclusion of the accumulated contribution of function values at past times. In order to lessen the computational load while maintaining the…
Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…
Adaptive second-order Crank-Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional Molecular Beam Epitaxial models with Caputo's derivative. Based on the piecewise…
We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known…
An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of…
The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the…
In this work, we investigate a fractional-order tumor growth model aimed at capturing memory effects and nonlocal temporal dynamics inherent to tumor evolution. The model is formulated using Caputo fractional derivatives and incorporates…
Mathematical models that accurately predict the mechanical behavior of blood can contribute to the development of biomedical devices and medications which are relevant in clinical applications. The models existing in the literature are…
Effective medical simulators necessitate realistic haptic rendering of biological tissues that exhibit viscoelastic material properties, such as creep and stress relaxation. Fractional-order models provide an effective means of describing…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…
Constitutive models that describe the mechanical behavior of soft tissues have advanced greatly over the past few decades. These expert models are generalizable and require the calibration of a number of parameters to fit experimental data.…
As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the…
The aim of this paper is to present a linear viscoelastic model based on Prabhakar fractional operators. In particular, we propose a modification of the classical fractional Maxwell model, in which we replace the Caputo derivative with the…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
In this paper, we propose a fast second-order approximation to the variable-order (VO) Caputo fractional derivative, which is developed based on $L2$-$1_\sigma$ formula and the exponential-sum-approximation technique. The fast evaluation…
We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are especially important for physical and biological systems that…
We present an efficient algorithm for the evaluation of the Caputo fractional derivative $_0^C\!D_t^\alpha f(t)$ of order $\alpha\in (0,1)$, which can be expressed as a convolution of $f'(t)$ with the kernel $t^{-\alpha}$. The algorithm is…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…