Unified Software Interface for Numerical Evaluation of Integrals and Derivatives of Fractional Order

2020 ◽  
Author(s):  
Tomas Skovranek ◽  
Matthew Harker ◽  
Igor Podlubny ◽  
Paul O'Leary ◽  
Ivo Petras
Keyword(s):  
Fractional Order ◽  
Numerical Evaluation ◽  
Software Interface ◽  
Derivatives Of

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 Mathematical modelling of the mass-spring-damper system - A fractional calculus approach

2012 ◽  
Vol 22 (5) ◽  
pp. 5-11 ◽  
Author(s):  
José Francisco Gómez Aguilar ◽  
Juan Rosales García ◽  
Jesus Bernal Alvarado ◽  
Manuel Guía
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Mathematical Modelling ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Time Derivative ◽  
System A ◽  
Fractional Differential ◽  
Mass Spring ◽  
Derivatives Of

In this paper the fractional differential equation for the mass-spring-damper system in terms of the fractional time derivatives of the Caputo type is considered. In order to be consistent with the physical equation, a new parameter is introduced. This parameter char­acterizes the existence of fractional components in the system. A relation between the fractional order time derivative and the new parameter is found. Different particular cases are analyzed

scholarly journals An analytical solution for solving a new wave equation within Lorenzo-Hartley kernel

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 3739-3744
Author(s):  
Feng Gao
Keyword(s):  
Wave Equation ◽  
Analytical Solution ◽  
Fractional Order ◽  
New Wave ◽  
Liouville Type ◽  
Derivatives Of

In this article we investigate the general fractional-order derivatives of the Riemann-Liouville type via Lorenzo-Hartley kernel, general fractional-order integrals and the new general fractional-order wave equation defined on the definite domain with the analytical soluton.

Digital Fractional Order Savitzky-Golay Differentiator and Its Application

2011 ◽  
Author(s):  
Dali Chen ◽  
Dingyu Xue ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Least Square ◽  
One Dimension ◽  
Order Derivative ◽  
Noisy Signal ◽  
Fractional Order Derivative ◽  
Least Square Fitting ◽  
Image Enhancing ◽  
The One ◽  
Derivatives Of

Firstly the one-dimension digital fractional order Savitzky-Golay differentiator (1-D DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order, is proposed to estimate the fractional order derivative of the noisy signal. The polynomial least square fitting technology and the Riemann-Liouville fractional order derivative definition are used to ensure robust and accuracy. Experiments demonstrate that 1-D DFOSGD can estimate the fractional order derivatives of both ideal signal and noisy signal accurately. Secondly, the two-dimension DFOSGD is obtained from 1-D DFOSGD by defining a group of direction operators, and a new image enhancing method based on 2-D DFOSGD is presented. Experiments demonstrate that 2-D DFOSGD has very good performance on image enhancement.

scholarly journals A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Aydin Secer
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Special Functions ◽  
Advantages And Disadvantages ◽  
Derivatives Of

The purpose of this note is to present the different fractional order derivatives definition that are commonly used in the literature on one hand and to present a table of fractional order derivatives of some functions in Riemann-Liouville sense On other the hand. We present some advantages and disadvantages of these fractional derivatives. And finally we propose alternative fractional derivative definition.

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