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A bibliography on numerical inversion of the laplace transform and applications: A supplement
1976
Journal of Computational and Applied Mathematics
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Partial fraction expansion of a transfer function matrix with one multiple eigenvalue. Elect. Lett. 6 (1970), 215-216. 1972 1. Astrakhan, V. I. ...
On inversion of the Laplace transformation by means of a step function. Ph.D. Thesis, The University of Texas Ot Austin, U.S.A., 1960.
4. N-Nagy, F. L.; A1-Tikriti, M. N. ...
doi:10.1016/0771-050x(76)90009-7
fatcat:hdweqvhdlbd7xmfyinpfmpvqv4
Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus
2021
Fractal and Fractional
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We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and a Sinc-Gaussian based method. ...
The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. ...
Acknowledgments: I acknowledge the inspiring discussions and valuable ideas by Frank Stenger.
Conflicts of Interest: There is no conflict of interest. ...
doi:10.3390/fractalfract5020043
fatcat:pwwvosogl5durl7cmfnjn4ihlm
Accuracy of rational-function approximations for linear transonic unsteady aerodynamics
1993
Journal of Aircraft
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The generalized Theodorsen function is a Laplace transform composed of tanscendental functions and it has no closed-form inverse transform. ...
dr 0<B<1 (4)
D°[x(t)] = r
Where [ denotes the gamma function instead of circulation. The Laplace transform of Eq. (4) reveals the operative prop- erty of fractional order differentiation:
L{D? ...
doi:10.2514/3.46445
fatcat:5ldvkx37pjdrhgcsoxmj4yctby
Sinc-Approximations of Fractional Operators: A Computing Approach
2015
Mathematics
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We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. ...
Several examples demonstrate the application of the method to different practical problems. ...
Acknowledgments We acknowledge the support by N. Südland in symbolic computer algebra calculations with Fractional Calculus. ...
doi:10.3390/math3020444
fatcat:fml4u3kax5ey7hhjpfwpuy3elm
Modeling and administration scheduling of fractional-order pharmacokinetic systems
[article]
2017
arXiv
pre-print
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In this paper we present several ways to simulate such fractional-order pharmacokinetic models and we evaluate their accuracy and complexity on a fractional-order pharmacokinetic model of Amiodarone, an ...
Fractional-order dynamical systems were recently introduced in the field of pharmacokinetics where they proved powerful tools for modeling the absorption, disposition, distribution and excretion of drugs ...
transfer functions and (iii) numerical approximation schemes in the discrete time domain, (iv) the numerical inverse Laplace transformation. 2.3.1 Analytical solutions. ...
arXiv:1701.08668v1
fatcat:wcsb2r5pmrg5bhgwlnuo7ehgj4
Construction of open-loop electromechanical system fundamental matrix and its application for calculation of state variables transients
2020
Energy Engineering and Control Systems
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It is shown that the description of processes in systems with fractional derivatives based on the transient matrix and the representation of the fractional derivative in the form of Caputo-Fabrizio makes ...
It is shown that the expression for the transition matrix as a matrix exponent completely corresponds to the expression found by means of the inverse matrix and based on the use of the signal graph. ...
function ( ), which is found by the inverse Laplace transform of ( ) in the form of an inverse matrix will look the same. ( ) [ ( ) [ ] ] (6) Now we find the transient matrix as a matrix exponent for ...
doi:10.23939/jeecs2020.02.110
fatcat:yblq63axpjaqbdjpnscbrgw3xa
Numerical Method for Inverse Laplace Transform with Haar Wavelet Operational Matrix
2014
Malaysian Journal of Fundamental and Applied Sciences
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Moreover, this work gives an alternative way to find the solution for inversion of Laplace transform in a faster way. ...
We present a numerical method for inversion of Laplace transform using the method of Haar wavelet operational matrix for integration. ...
ACKNOWLEDGEMENT The authors thank the Mathematical Science Institute, Faculty of Science, University of Malaya for funding partially the cost to be able to join RAFSS. ...
doi:10.11113/mjfas.v8n4.149
fatcat:wdamwel2xjgdjdblbvcdx3urda
Coefficients Identification in Fractional Diffusion Models by the Method of Time Integral Characteristics
2016
Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software
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Inverse problems of identication of the fractional diusivity and the order of fractional dierentiation are considered for linear fractional anomalous diusion equations with the Riemann Liouville and Caputo ...
It is shown that the inverse problems under consideration are reduced to the identication problem for a new single parameter which is formed by the fractional diusivity, the order of fractional dierentiation ...
If a function is dened by the table then a spline approximation is used. The order of spline approximation can be changed by user (the cubic spline approximation is used as a default setting). ...
doi:10.14529/mmp160309
fatcat:u5riawfk55ghngakkbxtsslfoy
Analysis of solutions of the 1D fractional Cattaneo heat transfer equation
2021
Journal of Applied Mathematics and Computational Mechanics
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The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. ...
The effect of the order of the fractional derivative on the temperature distribution is investigated. ...
) Expressing the above solution containing the inverse Laplace transform by the form of analytical function seems to be a complex problem. ...
doi:10.17512/jamcm.2021.4.08
fatcat:qj6vvltelzgwbbn527bds3fqhm
Fractional stochastic description of hinge motions in single protein molecules
2011
Chinese Science Bulletin
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noise with a power-law correlation. ...
ribonuclease H 1 . fractional Langevin dynamics, protein hinge motion, Laplace inversion Citation: Wang J Z. ...
transfer function G(t) in eqs. (7)−(11) can be obtained by performing an inverse Laplace transform with respect to ( ) G s . ...
doi:10.1007/s11434-010-4218-9
fatcat:mjp45gkvpbeglov2n5sgyiyciu
Fractional calculus in pharmacokinetics
2017
Journal of Pharmacokinetics and Pharmacodynamics
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2019 pre-print arXiv:1904.10556v1 fatcat:vpxsb4ffwnenpoyt4ihrmw4tqm
The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the drug amiodarone and the associated irregular accumulation patterns ...
We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics ...
Numerical inverse Laplace The inverse Laplace transform of a transfer function F (s) -on the Laplace s-domain -is given by the complex integral f (t) = L −1 {F }(t) = lim T →∞ 1 2πi σ+iT σ−iT e st F (s ...
doi:10.1007/s10928-017-9547-8
pmid:28975496
fatcat:6v74ekcsvve5lc2hmvzrjwslkm
Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem
2021
Symmetry
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A solution of the initial-boundary problem is determined by using the Fourier–Laplace transform technique. The final form of solution is given in a form of a series. ...
One of the properties of the derived fundamental solution of the considered problem with the initial condition expressed be the Dirac delta function is that it is symmetrical. ...
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/sym13081333
fatcat:3noi5iqw3jggba6u66sczd6kb4
A General Card-Program for the Evaluation of the Inverse Laplace Transform
1955
Journal of the ACM
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This goal was met, since the only restrictions on the transfer function are that it be a rational algebraic fraction with numerator of any order up to fifteen, and a denominator of any order up to sixteen ...
JOURNAL
A GENERAL CARD-PROGRAM FOR THE EVALUATION
OF THE INVERSE LAPLACE TRANSFORM*
By C. K. TITUS Westinghouse Electric Corporation, Baltimore, Md. ...
doi:10.1145/320789.320792
fatcat:gtdhg7ymnvdlnh234xmibjs5oy
Properties of Fractional-Order Magnetic Coupling
2020
Energies
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The application of fractional-order differential calculus makes it possible to model them in a simple way by appropriate selection of coefficients and fractional-order derivatives. ...
The difficulties connected with the analysis of two coils in dynamic states, resulting from the classical approach, provided motivation for studying the properties of fractional-order magnetic coupling ...
The basic methods used to determine the inverse Laplace transform of fractional-order systems allow the approximation of the s factor by the quotient of polynomials with integer powers. ...
doi:10.3390/en13071539
fatcat:gorhtpskabctppvo3wzp6uo77i
New Design Method for Fractional Order Proportional Integral (FO-PI) Controller of 3x3 Multivariable Systems
2020
Algerian journal of signals and systems
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The irrational transfer function of the fractional operator is performed by means of diffusive representation and allows to formulate the optimization problem as a function of fractional order. ...
This paper presents a new design method of Fractional Order Proportional Integral Controller (FO-PI) for 3x3 multivariable system (three-input-three-output). ...
In other words, ( ) the representation is obtained directly by the inverse Laplace transformation of the impulse response ( ). ...
doi:10.51485/ajss.v5i1.99
fatcat:yxhequfvejeazbqepvz7f56cf4
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