The random walk's guide to anomalous diffusion: a fractional dynamics approach

R Metzler, J Klafter - Physics reports, 2000 - Elsevier
Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type
are presented as a useful approach for the description of transport dynamics in complex …

The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

R Metzler, J Klafter - Journal of Physics A: Mathematical and …, 2004 - iopscience.iop.org
Fractional dynamics has experienced a firm upswing during the past few years, having been
forged into a mature framework in the theory of stochastic processes. A large number of …

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 …

[BOOK][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 …

Fractional viscoelastic models for power-law materials

A Bonfanti, JL Kaplan, G Charras, A Kabla - Soft Matter, 2020 - pubs.rsc.org
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 …

Basic theory of fractional differential equations

V Lakshmikantham, AS Vatsala - Nonlinear Analysis: Theory, Methods & …, 2008 - Elsevier
In this paper, the basic theory for the initial value problem of fractional differential equations
involving Riemann–Liouville differential operators is discussed employing the classical …

[BOOK][B] Topics in fractional differential equations

S Abbas, M Benchohra, GM N'Guérékata - 2012 - books.google.com
​​​ Topics in Fractional Differential Equations is devoted to the existence and uniqueness
of solutions for various classes of Darboux problems for hyperbolic differential equations or …

Detailed error analysis for a fractional Adams method

K Diethelm, NJ Ford, AD Freed - Numerical algorithms, 2004 - Springer
We investigate a method for the numerical solution of the nonlinear fractional differential
equation D* α y (t)= f (t, y (t)), equipped with initial conditions y (k)(0)= y 0 (k), k= 0, 1,...,⌈ …

A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions

RP Agarwal, M Benchohra, S Hamani - Acta Applicandae Mathematicae, 2010 - Springer
In this survey paper, we shall establish sufficient conditions for the existence and
uniqueness of solutions for various classes of initial and boundary value problem for …

[HTML][HTML] Existence of mild solutions for fractional neutral evolution equations

Y Zhou, F Jiao - Computers & Mathematics with Applications, 2010 - Elsevier
In this paper, by using the fractional power of operators and some fixed point theorems, we
discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain …