scholarly journals Inequalities of Kolmogorov type for fractional derivatives of multivariable functions

2021 ◽  
Vol 16 ◽  
pp. 3
Author(s):  
V.F. Babenko ◽  
T.V. Matveeva
Keyword(s):  
Fractional Derivatives ◽  
Sharp Inequality ◽  
Lipschitz Spaces ◽  
Kolmogorov Type ◽  
Variable Function ◽  
Derivatives Of ◽  
Marchaud Derivative

We prove new sharp inequality of Kolmogorov type that estimates the norm of mixed fractional Marchaud derivative of n-variable function by C-norm of this function and its norms in Lipschitz spaces.

scholarly journals On inequalities of Kolmogorov type for fractional derivatives of functions defined on the real domain

2021 ◽  
Vol 16 ◽  
pp. 28
Author(s):  
V.F. Babenko ◽  
M.S. Churilova
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Kolmogorov Type ◽  
The Real ◽  
Higher Derivative ◽  
Real Domain ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
New Inequalities

We obtain new inequalities that generalize known result of Geisberg, which was obtained for fractional Marchaud derivatives, to the case of higher derivatives, at that the fractional derivative is a Riesz one. The inequality with second higher derivative is sharp.

scholarly journals Exact inequalities of Kolmogorov type for Hadamard fractional derivatives of functions defined on half-line

2021 ◽  
Vol 18 ◽  
pp. 38
Author(s):  
V.F. Babenko ◽  
N.V. Parfinovich
Keyword(s):  
Fractional Derivatives ◽  
Half Line ◽  
Kolmogorov Type ◽  
Derivatives Of

New exact inequalities for Hadamard fractional derivatives of functions, defined on the half-line, are obtained.

scholarly journals Kolmogorov type inequalities for Hadamard fractional derivatives of functions defined on half-line, and their applications

2012 ◽  
Vol 20 ◽  
pp. 49
Author(s):  
V.F. Babenko ◽  
N.V. Parfinovich ◽  
A.A. Semirenko
Keyword(s):  
Fractional Derivatives ◽  
Half Line ◽  
Kolmogorov Type ◽  
Derivatives Of

For the norms of fractional Hadamard derivatives of functions defined on the half-line, the sharp Kolmogorov-type inequalities are obtained. Applications of these inequalities are given.

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.

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