The random walk's guide to anomalous diffusion: a fractional dynamics approach
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 …
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
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 …
forged into a mature framework in the theory of stochastic processes. A large number of …
Analysis of fractional differential equations
We discuss existence, uniqueness, and structural stability of solutions of nonlinear
differential equations of fractional order. The differential operators are taken in the Riemann …
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 …
treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation …
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 …
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 …
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 …
of solutions for various classes of Darboux problems for hyperbolic differential equations or …
Detailed error analysis for a fractional Adams method
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,...,⌈ …
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
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 …
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 …
discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain …