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 …

On history of mathematical economics: Application of fractional calculus

VE Tarasov - Mathematics, 2019 - mdpi.com
Modern economics was born in the Marginal revolution and the Keynesian revolution. These
revolutions led to the emergence of fundamental concepts and methods in economic theory …

[BOOK][B] Mittag-Leffler functions, related topics and applications

R Gorenflo, AA Kilbas, F Mainardi, SV Rogosin - 2020 - Springer
Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

[BOOK][B] Fractional calculus: models and numerical methods

D Baleanu, K Diethelm, E Scalas, JJ Trujillo - 2012 - books.google.com
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 …

[BOOK][B] Functional fractional calculus

S Das - 2011 - Springer
When a new extraordinary and outstanding theory is stated, it has to face criticism and
skeptism, because it is beyond the usual concept. The fractional calculus though not new …

[HTML][HTML] Finite difference approximations for fractional advection–dispersion flow equations

MM Meerschaert, C Tadjeran - Journal of computational and applied …, 2004 - Elsevier
Fractional advection–dispersion equations are used in groundwater hydrology to model the
transport of passive tracers carried by fluid flow in a porous medium. In this paper we …

The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique

S Djennadi, N Shawagfeh, MS Osman… - Physica …, 2021 - iopscience.iop.org
This research considers an inverse source problem for fractional diffusion equation that
containing fractional derivative with non-singular and non-local kernel, namely, Atangana …

[HTML][HTML] Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

Q Yang, F Liu, I Turner - Applied Mathematical Modelling, 2010 - Elsevier
In this paper, we consider the numerical solution of a fractional partial differential equation
with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE …

The use of finite difference/element approaches for solving the time-fractional subdiffusion equation

F Zeng, C Li, F Liu, I Turner - SIAM Journal on Scientific Computing, 2013 - SIAM
In this paper, two finite difference/element approaches for the time-fractional subdiffusion
equation with Dirichlet boundary conditions are developed, in which the time direction is …

Finite difference methods for two-dimensional fractional dispersion equation

MM Meerschaert, HP Scheffler, C Tadjeran - Journal of Computational …, 2006 - Elsevier
Fractional order partial differential equations, as generalizations of classical integer order
partial differential equations, are increasingly used to model problems in fluid flow, finance …