scholarly journals Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2856
Author(s):  
Tong Yuan ◽  
Hongli Yang ◽  
Ivan Ganchev Ivanov
Keyword(s):  
Laplace Transform ◽  
Fractional Derivatives ◽  
Electrical Circuits ◽  
Preliminary Results ◽  
Generalized Fractional Derivatives

Positive linear electrical circuits systems described by generalized fractional derivatives are studied in this paper. We mainly focus on the reachability and observability of linear electrical circuits systems. Firstly, generalized fractional derivatives and ρ-Laplace transform of f is presented and some preliminary results are provided. Secondly, the positivity of linear electrical circuits systems described by generalized fractional derivatives is investigated and conditions for checking positivity of the systems are derived. Thirdly, reachability and observability of the generalized fractional derivatives systems are studied, in which the ρ-Laplace transform of a Mittag-Leffler function plays an important role. At the end of the paper, illustrative electrical circuits systems are presented, and conclusions of the paper are presented.

scholarly journals Generalized fractional derivatives and Laplace transform

2020 ◽  
Vol 13 (3) ◽  
pp. 709-722 ◽  
Author(s):  
Fahd Jarad ◽  
◽  
Thabet Abdeljawad ◽  
Keyword(s):  
Laplace Transform ◽  
Fractional Derivatives ◽  
Generalized Fractional Derivatives

scholarly journals Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1665
Author(s):  
Fátima Cruz ◽  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Time Delay ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Fractional Operator ◽  
Different Types ◽  
Generalized Fractional Derivatives ◽  
Necessary And Sufficient ◽  
Distributed Order

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

ON A HIGH-PASS FILTER DESCRIBED BY LOCAL FRACTIONAL DERIVATIVE

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050031 ◽  
Author(s):  
KANG-JIA WANG
Keyword(s):  
Transfer Function ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Pass Filter ◽  
Electrical Circuits ◽  
Local Fractional Derivative ◽  
High Pass Filter ◽  
Fractal Space ◽  
High Pass

The local fractional derivative (LFD) has gained much interest recently in the field of electrical circuits. This paper proposes a non-differentiable (ND) model of high-pass filter described by the LFD, where the ND transfer function is obtained with the help of the local fractional Laplace transform, and its parameters and properties are studied. The obtained results reveal the sufficiency of the LFD for analyzing circuit systems in fractal space.

scholarly journals Opial typeLp-inequalities for fractional derivatives

2002 ◽  
Vol 31 (2) ◽  
pp. 85-95 ◽  
Author(s):  
G. A. Anastassiou ◽  
J. J. Koliha ◽  
J. Pecaric
Keyword(s):  
Fractional Derivatives ◽  
Continuous Functions ◽  
Taylor’S Formula ◽  
Integrable Functions ◽  
Generalized Fractional Derivatives ◽  
Taylor's Formula

This paper presents a class ofLp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor's formula, which enables us to relax restrictions on the orders of fractional derivatives.

scholarly journals Recent applications of fractional calculus to science and engineering

2003 ◽  
Vol 2003 (54) ◽  
pp. 3413-3442 ◽  
Author(s):  
Lokenath Debnath
Keyword(s):  
Dynamical Systems ◽  
Fractional Calculus ◽  
Control Theory ◽  
Numerical Computation ◽  
Fractional Derivatives ◽  
Fluid Flows ◽  
Voltage Divider ◽  
Science And Engineering ◽  
Electrical Circuits ◽  
Fractional Derivatives And Integrals

This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integrals.

POTENTIALS OF ARBITRARY FORCES WITH FRACTIONAL DERIVATIVES

2004 ◽  
Vol 19 (17n18) ◽  
pp. 3083-3092 ◽  
Author(s):  
EQAB M. RABEI ◽  
TAREQ S. ALHALHOLY ◽  
AKRAM ROUSAN
Keyword(s):  
Laplace Transform ◽  
General Formula ◽  
Fractional Derivatives ◽  
Fractional Integrals ◽  
Hamiltonian Mechanics ◽  
Dissipative Effects ◽  
Special Cases ◽  
Exact Agreement ◽  
The Laplace Transform ◽  
Lagrangian And Hamiltonian Mechanics

The Laplace transform of fractional integrals and fractional derivatives is used to develop a general formula for determining the potentials of arbitrary forces: conservative and nonconservative in order to introduce dissipative effects (such as friction) into Lagrangian and Hamiltonian mechanics. The results are found to be in exact agreement with Riewe's results of special cases. Illustrative examples are given.

Generalized fractional derivatives and their applications to mechanical systems

2014 ◽  
Vol 85 (9-10) ◽  
pp. 1307-1320 ◽  
Author(s):  
John T. Katsikadelis
Keyword(s):  
Fractional Derivatives ◽  
Mechanical Systems ◽  
Generalized Fractional Derivatives
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