Results 21 to 30 of about 974 (111)

On the fractional Poisson process and the discretized stable subordinator [PDF]

, 2015
The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes.
Gorenflo, Rudolf, Mainardi, Francesco
core   +3 more sources

A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations

Results in Physics
In this paper, we introduce the ψ-Hilfer fractional version of nonlinear Galilei-invariant advection–diffusion equations in one and two dimensions. A new type of basic functions, namely the ψ-Chebyshev cardinal functions (CFs), is introduced to establish
M.H. Heydari, M. Razzaghi, M. Bayram
doaj   +1 more source

Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation

, 2004
A detailed study is presented for a large class of uncoupled continuous-time random walks (CTRWs). The master equation is solved for the Mittag-Leffler survival probability.
A. Compte, A.I. Saichev, E. Barkai, E. Barkai, E. Barkai, E. Scalas, E. Scalas, E.W. Montroll, E.W. Montroll, Enrico Scalas, F. Mainardi, F. Mainardi, F. Mainardi, Francesco Mainardi, G.H. Weiss, G.M. Zaslavsky, H.C. Fogedby, H.E. Roman, I.M. Sokolov, J. Klafter, J. Klafter, J. Klafter, J. Masoliver, J.K.E. Tunaley, J.K.E. Tunaley, J.K.E. Tunaley, M. Kotulski, M. Raberto, M.F. Shlesinger, M.F. Shlesinger, M.M. Meerschaert, R. Hilfer, R. Hilfer, R. Hilfer, R. Hilfer, R. Hilfer, R. Kutner, R. Kutner, R. Metzler, R. Metzler, R. Metzler, Rudolf Gorenflo, T. Huillet, T. Huillet, V. Balakrishnan, V.V. Uchaikin, V.V. Uchaikin, W.R. Schneider   +47 more
core   +1 more source

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation [PDF]

, 2008
We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of ...
A. I. Saichev, D. ben Avraham, Daniel Fulger, Enrico Scalas, G. Germano, Guido Germano, I. Podlubny, J. von Neumann, L. Devroye, N. J. Ford, R. Gorenflo, S. G. Samko, S. Kotz, S. Mittnik, T. A. M. Langlands, T. J. Kozubowski, W. Feller, W. H. Press   +17 more
core   +2 more sources

Controllability of psi-Hilfer fractional differential equations with infinite delay via measure of noncompactness

Nonlinear Analysis
In this article, we study the controllability of ψ-Hilfer fractional differential equations with infinite delay. Sufficient conditions for controllability results are obtained by using the notion of the measure of noncompactness and the Mönch fixed ...
Inzamamul Haque, Javid Ali, Juan J. Nieto   +2 more
doaj   +1 more source

On a Coupled Differential System Involving (k,ψ)-Hilfer Derivative and (k,ψ)-Riemann–Liouville Integral Operators

Axioms, 2023
We investigate a nonlinear, nonlocal, and fully coupled boundary value problem containing mixed (k,ψ^)-Hilfer fractional derivative and (k,ψ^)-Riemann–Liouville fractional integral operators.
Ayub Samadi, Sotiris K. Ntouyas, Bashir Ahmad, Jessada Tariboon   +3 more
doaj   +1 more source

Existence and Stability for Fractional Differential Equations with a ψ–Hilfer Fractional Derivative in the Caputo Sense

Mathematics
This article aims to explore the existence and stability of solutions to differential equations involving a ψ-Hilfer fractional derivative in the Caputo sense, which, compared to classical ψ-Hilfer fractional derivatives (in the Riemann–Liouville sense),
Wenchang He, Yuhang Jin, Luyao Wang, Ning Cai, Jia Mu   +4 more
doaj   +1 more source

Existence and Ulam stability results of a coupled system for terminal value problems involving ψ-Hilfer fractional operator

Advances in Difference Equations, 2020
The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at hand are investigated.
Mohammed S. Abdo, Kamal Shah, Satish K. Panchal, Hanan A. Wahash   +3 more
doaj   +1 more source

Existence and Attractivity of Mild Solutions for Fractional Diffusion Equations Involving the Regularized ψ-Hilfer Fractional Derivatives

Axioms
The regularized ψ-Hilfer derivative within the sense of Caputo is an improved version of the ψ-Hilfer fractional derivative, primarily because it addresses the issue where the initial conditions of problems involving the ψ-Hilfer fractional derivative ...
Luyao Wang, Yuhang Jin, Wenchang He, Jia Mu   +3 more
doaj   +1 more source

Infrared spectroscopy of diatomic molecules - a fractional calculus approach

, 2012
The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative.
Dirac P. A. M., Eid R., Erdelyi A., Greiner W., Herrmann R., Herrmann R., Herzberg G., Huygens C., Khunrath H., Krause K., Lissajous J. A., Lusztig R., Messiah A., Oldham K. B., Parisi G., Podlubny I., RICHARD HERRMANN, Rubin B., Seybold H. J., Villeneuve D. M., Whitten K. W.   +20 more
core   +1 more source