On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

2012 ◽  
Vol 20 (3) ◽  
Author(s):  
Mohamed Ait Ouahra ◽  
Abdelghani Kissami ◽  
Hanae Ouahhabi
Keyword(s):  
Local Time ◽  
Fractional Derivatives ◽  
Stable Process ◽  
Symmetric Stable Process ◽  
Derivatives Of

On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

2014 ◽  
Vol 22 (2) ◽  
Author(s):  
Mohamed Ait Ouahra ◽  
Abdelghani Kissami ◽  
Hanae Ouahhabi
Keyword(s):  
Local Time ◽  
Fractional Derivatives ◽  
Stable Process ◽  
Symmetric Stable Process ◽  
Derivatives Of

Abstract.In this paper we prove two main results. The first one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index

scholarly journals Extension of Mikhlin multiplier theorem to fractional derivatives and stable processes

2018 ◽  
Vol 21 (2) ◽  
pp. 486-508
Author(s):  
Deniz Karlı
Keyword(s):  
Infinitesimal Generator ◽  
Fractional Derivatives ◽  
Stable Process ◽  
Stable Processes ◽  
Multiplier Theorem ◽  
Symmetric Stable Process ◽  
Integral Forms

Abstract In this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between fractional derivatives and stable processes and prove a version of Mikhlin theorem under a condition given in terms of the infinitesimal generator of symmetric stable process. The classical Mikhlin theorem is shown to be a corollary of this new generalized version in this paper.

scholarly journals A Note on the Generalized Relativistic Diffusion Equation

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1009
Author(s):  
Luisa Beghin ◽  
Roberto Garra
Keyword(s):  
Fourier Transform ◽  
Fundamental Solution ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Stable Process ◽  
Caputo Fractional Derivatives ◽  
The Fourier Transform ◽  
Derivatives Of

We study here a generalization of the time-fractional relativistic diffusion equation based on the application of Caputo fractional derivatives of a function with respect to another function. We find the Fourier transform of the fundamental solution and discuss the probabilistic meaning of the results obtained in relation to the time-scaled fractional relativistic stable process. We briefly consider also the application of fractional derivatives of a function with respect to another function in order to generalize fractional Riesz-Bessel equations, suggesting their stochastic meaning.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

scholarly journals Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 475
Author(s):  
Ewa Piotrowska ◽  
Krzysztof Rogowski
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Electric Circuit ◽  
Theoretical Models ◽  
Time Domain Analysis ◽  
Electrical Circuit ◽  
State Variable ◽  
State Space System ◽  
Derivatives Of ◽  
Different Order

The paper is devoted to the theoretical and experimental analysis of an electric circuit consisting of two elements that are described by fractional derivatives of different orders. These elements are designed and performed as RC ladders with properly selected values of resistances and capacitances. Different orders of differentiation lead to the state-space system model, in which each state variable has a different order of fractional derivative. Solutions for such models are presented for three cases of derivative operators: Classical (first-order differentiation), Caputo definition, and Conformable Fractional Derivative (CFD). Using theoretical models, the step responses of the fractional electrical circuit were computed and compared with the measurements of a real electrical system.

scholarly journals Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Fractional Derivatives ◽  
Three Dimensional ◽  
Lattice Models ◽  
Fractional Diffusion ◽  
Lattice Diffusion ◽  
Diffusion Equations ◽  
Difference Operators ◽  
Fractional Diffusion Equations ◽  
Nonlocal Media ◽  
Derivatives Of

Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grünwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe long-range jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the Grünwald-Letnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of Grünwald-Letnikov type. The suggested lattice diffusion equations can be considered as a new microstructural basis of space-fractional diffusion in nonlocal media.

Sign in / Sign up

Export Citation Format

Share Document