scholarly journals Integrals and derivatives of fractional order based on Laplace type integral transformations with applications

2021 ◽  
Vol 53 (2) ◽  
pp. 114-124
Author(s):  
Oleg Iaremko ◽  
Natalia Iaremko
Keyword(s):  
Fractional Order ◽  
Integral Transformations ◽  
Type Integral ◽  
Derivatives Of ◽  
Laplace Type

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.

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

scholarly journals Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Integral Equation ◽  
Fractional Order ◽  
Operational Calculus ◽  
Point Of View ◽  
Alternative Method ◽  
Type Integral

This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.

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.

An Application to H2+ of Laplace Type Integral Transform and its Inverse

1985 ◽  
Vol 40 (3) ◽  
pp. 246-250 ◽  
Author(s):  
M. Primorac ◽  
K. Kovačević
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Integral Transform ◽  
Integral Transformation ◽  
Inverse Transform ◽  
Type Integral ◽  
Analytical Formulae ◽  
Molecular Computations ◽  
Laplace Type

Laplace type integral transformation (LIT) has been applied to wavefunctions. The effect of the inverse transform is also discussed. LIT wavefunctions are tested in the calculation of the ground-state energy of H2+, where the untransformed functions were 1s, 12s, 123s and 1234s- STO. The results presented here show that LIT wavefunctions are applicable in molecular computations. The analytical formulae for two-centre one-electron integrals over LIT wavefunctions are derived by use of a Barnett-Coulson-like expansion of rbN (rb + p)-v.

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