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Journal articles on the topic 'Inverse Laplace transform'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Ruehr, O. G., and W. R. Young. "An Inverse Laplace Transform." SIAM Review 30, no. 4 (1988): 652. http://dx.doi.org/10.1137/1030146.

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2

Clarkson, M. "MACSYMS's inverse Laplace transform." ACM SIGSAM Bulletin 23, no. 1 (1989): 33–38. http://dx.doi.org/10.1145/66062.66066.

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3

Hernández-Galeana, A. "On the Inverse Laplace Transform." Kathmandu University Journal of Science, Engineering and Technology 9, no. 1 (2013): 161–64. http://dx.doi.org/10.3126/kuset.v9i1.63856.

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4

Kamran, Farman Ali Shah, Wael Hosny Fouad Aly, Hasan Aksoy, Fahad M. Alotaibi, and Ibrahim Mahariq. "Numerical Inverse Laplace Transform Methods for Advection-Diffusion Problems." Symmetry 14, no. 12 (2022): 2544. http://dx.doi.org/10.3390/sym14122544.

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Partial differential equations arising in engineering and other sciences describe nature adequately in terms of symmetry properties. This article develops a numerical method based on the Laplace transform and the numerical inverse Laplace transform for numerical modeling of diffusion problems. This method transforms the time-dependent problem to a corresponding time-independent inhomogeneous problem by employing the Laplace transform. Then a local radial basis functions method is employed to solve the transformed problem in the Laplace domain. The main feature of the local radial basis functio

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5

González-Santander, Juan Luis, and Alexander Apelblat. "A Note on Some Novel Laplace and Stieltjes Transforms Associated with the Relaxation Modulus of the Andrade Model." Axioms 13, no. 9 (2024): 647. http://dx.doi.org/10.3390/axioms13090647.

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In the framework of linear viscoelasticity, the authors have previously calculated a novel inverse Laplace transform involving the Mittag–Leffler function in order to calculate the relaxation modulus in the Andrade model. Here, we generalize this result, calculating the inverse Laplace transform of a given function Fα,βs by using two different approaches: the Bromwich integral and the decomposition of Fα,βs in simple fractions. From both calculations, we obtain a set of novel Laplace and Stieltjes transforms.

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Kamran, Sharif Ullah Khan, Salma Haque, and Nabil Mlaiki. "On the Approximation of Fractional-Order Differential Equations Using Laplace Transform and Weeks Method." Symmetry 15, no. 6 (2023): 1214. http://dx.doi.org/10.3390/sym15061214.

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Differential equations of fractional order arising in engineering and other sciences describe nature sufficiently in terms of symmetry properties. In this article, a numerical method based on Laplace transform and numerical inverse Laplace transform for the numerical modeling of differential equations of fractional order is developed. The analytic inversion can be very difficult for complex forms of the transform function. Therefore, numerical methods are used for the inversion of the Laplace transform. In general, the numerical inverse Laplace transform is an ill-posed problem. This difficult

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Baumann, Gerd. "Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus." Fractal and Fractional 5, no. 2 (2021): 43. http://dx.doi.org/10.3390/fractalfract5020043.

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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. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to

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8

Sharma, M. D., and S. Nain. "Numerical evaluation of inverse integral transforms: Dynamic response of elastic materials." International Journal of Engineering, Science and Technology 12, no. 2 (2020): 29–34. http://dx.doi.org/10.4314/ijest.v12i2.4.

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This study discusses the use of numerical integration in evaluating the improper integrals appearing as inverse integral transforms of non-analytic functions. These transforms appear while studying the response of various sources in an elastic medium through integral transform method. In these studies, the inverse Fourier transforms are solved numerically without bothering about the singularities and branch points in the corresponding integrands. References on numerical integration cited in relevant papers do not support such an evaluation but suggest contrary. Approximation of inverse Laplace

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9

Biswas, T., and Satish D. Joglekar. "Inverse Laplace transform and perturbation theory." Journal of Mathematical Physics 40, no. 1 (1999): 369–82. http://dx.doi.org/10.1063/1.532788.

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10

Pintarelli, Dra María B. "Solution of a system of differential equations with constant coefficients using in-verse moments problem techniques." International Journal of Applied Mathematical Research 7, no. 3 (2019): 71. http://dx.doi.org/10.14419/ijamr.v7i3.12550.

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It is known that given a system of simultaneous linear differential equations with constant coefficients you can apply the Laplace method to solve it. The Laplace transforms are found and the problem is reduced to the resolution of an algebraic system of equations of the determining functions, and applying the inverse transformation the generating functions are determined, solutions of the given system. This implies the need to know the analytical form of the inverse transform of the function. In this case the initial conditions consist in knowing the value that the generating function and its

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11

Meganathan, M., Thabet Abdeljawad, G. Britto Antony Xavier, and Fahd Jarad. "n-Dimensional Fractional Frequency Laplace Transform by the Inverse Difference Operator." Mathematical Problems in Engineering 2020 (August 24, 2020): 1–11. http://dx.doi.org/10.1155/2020/6529698.

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With the study of extensive literature on the Laplace transform with one and two variables and its properties, applications are available, but there is no work on n-dimensional Laplace transform. In this research article, we define n-dimensional fractional frequency Laplace transform with shift values. Several theorems are derived with properties of the Laplace transform. The results are numerically analyzed and discussed through MATLAB.

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12

Horvath, Illes, Andras Meszaros, and Miklos Telek. "Optimized numerical inverse Laplace transformation." ACM SIGMETRICS Performance Evaluation Review 50, no. 2 (2022): 36–38. http://dx.doi.org/10.1145/3561074.3561087.

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Among the numerical inverse Laplace transformation (NILT) methods, those that belong to the Abate-Whitt framework (AWF) are considered to be the most efficient ones currently. It is a characteristic feature of the AWF NILT procedures that they are independent of the transform function and the time point of interest. In this work we propose an NILT procedure that goes beyond this limitation and optimize the accuracy of the NILT utilizing also the transform function and the time point of interest.

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13

Zill, E. Huma, Ul Rahman Jamshaid, Suleman Muhammad, and Anjum Naveed. "Cryptographic method based on natural-elzaki transform." i-manager’s Journal on Mathematics 11, no. 1 (2022): 39. http://dx.doi.org/10.26634/jmat.11.1.18511.

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Securing data in this era of technology is the most challenging task. Cryptography is a practice of different techniques and methodologies for data confidentiality, data integrity, authentication, and non-repudiation. Many mathematical techniques are being used in cryptography from ancient times. The Laplace integral transforms and its inverse forms gain significant importance to design cryptographic methods. In this work, we propose cryptography methodology based on Natural and Elzaki transform and this study comprises a unique structure that provides Laplace-Elzaki and Sumudu-Elzaki methodol

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14

Lee, Z. Y., and C. L. Chang. "Generalized coupled transient thermoelastic problem of multilayered spheres by the hybrid numerical method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 217, no. 12 (2003): 1315–23. http://dx.doi.org/10.1243/095440603322769956.

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This paper deals with axisymmetric quasi-static coupled thermoelastic problems for multilayered spheres. Laplace transforms and finite difference methods are used to analyse the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions are obtained for the temperature and thermal deformation distributions for the transient and steady state. It is demonstrated that the computational procedures est

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15

Dhunde, Ranjit R. "Double Laplace Transform Method for Solving Fractional Fourth-Order Partial Integro-Differential Equations with Weakly Singular Kernel." Indian Journal Of Science And Technology 17, no. 36 (2024): 3712–18. http://dx.doi.org/10.17485/ijst/v17i36.2005.

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Objectives: To investigates the solutions of fourth order partial integro-differential equations with high-order non-integer derivatives and weakly singular kernels. Methods: Weakly singular kernels present challenges in both analytical and numerical treatments due to their intricate behaviour near singular points. In this article, we introduce a novel approach utilizing the double Laplace transform method to effectively address these challenges. Findings: By solving a series of precise and understandable examples, the double Laplace transform clearly transforms the fractional partial integro-

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16

Ranjit, R. Dhunde. "Double Laplace Transform Method for Solving Fractional Fourth-Order Partial Integro-Differential Equations with Weakly Singular Kernel." Indian Journal of Science and Technology 17, no. 36 (2024): 3712–18. https://doi.org/10.17485/IJST/v17i36.2005.

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Abstract <strong>Objectives:</strong> To investigates the solutions of fourth order partial integro-differential equations with high-order non-integer derivatives and weakly singular kernels. <strong>Methods:</strong> Weakly singular kernels present challenges in both analytical and numerical treatments due to their intricate behaviour near singular points. In this article, we introduce a novel approach utilizing the double Laplace transform method to effectively address these challenges. <strong>Findings:</strong> By solving a series of precise and understandable exam

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17

Saltas, Vassilios, Vassilios Tsiantos, and Dimitrios Varveris. "Mathematic Attributions of Laplace Transform." European Journal of Mathematics and Statistics 3, no. 6 (2022): 8–19. http://dx.doi.org/10.24018/ejmath.2022.3.6.173.

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The purpose of this work is to define the Laplace transform and the Laplace inverse transformation, to describe their basic properties and to calculate the corresponding transforms of selected functions. To achieve these, the concept of the real function image is first defined, and in particular the conversion of the complex variable function. The examples used are initially pure mathematics, followed by reference to the practical application of these two transformations since they relate to the conversion of a continuous time signal into a complex variable function.

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18

Younis, Jihad, Bouchenak Ahmed, Mazin AlJazzazi, Rasha Al Hejaj, and Hassen Aydi. "Existence and Uniqueness Study of the Conformable Laplace Transform." Journal of Mathematics 2022 (April 26, 2022): 1–7. http://dx.doi.org/10.1155/2022/4554065.

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This paper tackles the topic of conformable Laplace transform. The authors aim at discussing its existence by exploring and providing the kind of functions that possess a conformable Laplace transform. Furthermore, the comparison theorem of conformable improper integrals is presented to further explain and justify the existence of conformable Laplace transform for some functions. The uniqueness is also established in order to determine the inverse of conformable Laplace transform for functions. Moreover, we present a table of the conformable Laplace transform of the usual functions. Finally, a

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Younis, Jihad, Bouchenak Ahmed, Mazin AlJazzazi, Rasha Al Hejaj, and Hassen Aydi. "Existence and Uniqueness Study of the Conformable Laplace Transform." Journal of Mathematics 2022 (April 26, 2022): 1–7. http://dx.doi.org/10.1155/2022/4554065.

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This paper tackles the topic of conformable Laplace transform. The authors aim at discussing its existence by exploring and providing the kind of functions that possess a conformable Laplace transform. Furthermore, the comparison theorem of conformable improper integrals is presented to further explain and justify the existence of conformable Laplace transform for some functions. The uniqueness is also established in order to determine the inverse of conformable Laplace transform for functions. Moreover, we present a table of the conformable Laplace transform of the usual functions. Finally, a

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20

Yavuz, Mehmet, and Necati Ozdemir. "Numerical inverse Laplace homotopy technique for fractional heat equations." Thermal Science 22, Suppl. 1 (2018): 185–94. http://dx.doi.org/10.2298/tsci170804285y.

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In this paper, we have aimed the numerical inverse Laplace homotopy technique for solving some interesting 1-D time-fractional heat equations. This method is based on the Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method. Firstly, we have applied to the fractional 1-D PDE by using He?s polynomials. Then we have used Laplace transform method and discussed how to solve these PDE by using Laplace homotopy perturbation method. We have declared that the proposed model is very efficient and powerful technique in finding approxi

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21

Tagliani, Aldo, and Yurayh Velásquez. "Inverse Laplace transform for heavy-tailed distributions." Applied Mathematics and Computation 150, no. 2 (2004): 337–45. http://dx.doi.org/10.1016/s0096-3003(03)00235-2.

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22

Choulli, M., and A. Zeghal. "Laplace transform approach for an inverse problem." Transport Theory and Statistical Physics 24, no. 9 (1995): 1353–67. http://dx.doi.org/10.1080/00411459508206028.

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23

Wituła, R. "Inverse Laplace Transform of Some Rational Functions." Acta Physica Polonica A 122, no. 5 (2012): 966–68. http://dx.doi.org/10.12693/aphyspola.122.966.

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24

Yamada, Hirofumi. "An Inverse Laplace Transform on Lattice Spacing." Chinese Physics Letters 30, no. 3 (2013): 031101. http://dx.doi.org/10.1088/0256-307x/30/3/031101.

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25

Contharteze Grigoletto, Eliana, and Edmundo Capelas de Oliveira. "A note on the inverse Laplace transform." Cadernos do IME - Série Matemática, no. 12 (November 22, 2018): 39–46. http://dx.doi.org/10.12957/cadmat.2018.34026.

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26

MacFarlane, W. A., D. Fujimoto та R. M. L. McFadden. "Inverse Laplace Transform Approaches to βNMR Relaxation". Journal of Physics: Conference Series 2462, № 1 (2023): 012015. http://dx.doi.org/10.1088/1742-6596/2462/1/012015.

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Abstract Spin lattice relaxation is the simplest type of βNMR measurement. The usual approach is to implant a pulse of hyperpolarized nuclei and monitor the time-resolved β-decay asymmetry, yielding the ensemble average spin-lattice relaxation. In the simplest case, the asymmetry decays exponentially with a characteristic time constant T 1, but this ideal is rarely obtained in practice. In most data, the relaxation is more complicated. This can be the result of multiple crystallographic sites for the implanted probe each having a distinct T 1. The sample may also be inhomogeneous due to: impur

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27

JAFARIZADEH, M. A., and R. SUFIANI. "INVESTIGATION OF CONTINUOUS-TIME QUANTUM WALKS VIA SPECTRAL ANALYSIS AND LAPLACE TRANSFORM." International Journal of Quantum Information 05, no. 04 (2007): 575–96. http://dx.doi.org/10.1142/s0219749907003043.

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Continuous-time quantum walk (CTQW) on a given graph is investigated using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with the graph. It is shown that the probability amplitude of observing the CTQW at a given site at time t is related to the inverse Laplace transformation of the Stieltjes function, namely, one can calculate the probability amplitudes only by taking the inverse laplace transform of the function iGμ(is), where Gμ(x) is the Stieltjes function of the graph. The prefe

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28

Bosch, Paul, Héctor José Carmenate García, José Manuel Rodríguez, and José María Sigarreta. "On the Generalized Laplace Transform." Symmetry 13, no. 4 (2021): 669. http://dx.doi.org/10.3390/sym13040669.

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In this paper we introduce a generalized Laplace transform in order to work with a very general fractional derivative, and we obtain the properties of this new transform. We also include the corresponding convolution and inverse formula. In particular, the definition of convolution for this generalized Laplace transform improves previous results. Additionally, we deal with the generalized harmonic oscillator equation, showing that this transform and its properties allow one to solve fractional differential equations.

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Çetınkaya, Süleyman, and Ali Demir. "Effects of the ARA transform method for time fractional problems." Mathematica Moravica 26, no. 2 (2022): 73–84. http://dx.doi.org/10.5937/matmor2202073c.

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The aim of this study is to establish the solutions of time fractional mathematical problems with the aid of new integral transforms called the ARA transform. The fractional derivative is taken in the sense of Liouville-Caputo derivative. The fractional partial differential equations are reduced into ordinary differential equations. Later solving this fractional equation and applying inverse the ARA transform, the solution is acquired. The implementation of this transform for fractional differential equations is very similar to the implementation of the Laplace transform. However, the ARA tran

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30

Chaurasia, V. B. L., and Hari Singh Parihar. "On the inverse Laplace transform of H-function associated with Feynman types integrals." Tamkang Journal of Mathematics 39, no. 4 (2008): 341–46. http://dx.doi.org/10.5556/j.tkjm.39.2008.8.

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The Laplace transform and its inverse are fundamental and powerful tools in solving boundary value problems occurring in the diverse fields of engineering. Here we will establish some useful formulas giving the inverse Laplace transform of various products of algebraic powers and $ \overline{H} $-function, involving one and more variables, which are unified and likely to have applications in several different areas.

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31

Kuhlman, Kristopher L. "Review of inverse Laplace transform algorithms for Laplace-space numerical approaches." Numerical Algorithms 63, no. 2 (2012): 339–55. http://dx.doi.org/10.1007/s11075-012-9625-3.

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32

Tang, He, Lan Zhang, Le Chang, and Wenke Sun. "Optimized approximate inverse Laplace transform for geo-deformation computation in viscoelastic Earth model." Geophysical Journal International 223, no. 1 (2020): 444–53. http://dx.doi.org/10.1093/gji/ggaa322.

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SUMMARY Integral transformations, especially the inverse Laplace transform, are powerful techniques for resolving a wide range of geophysical and geodynamic simulation problems in viscoelastic materials. The exact location or distribution range of poles of the image function in a complex plane is usually necessary for applying numerical algorithms such as contour integration. Unfortunately, there are innumerable poles (such as those of post-seismic deformations) in a realistic Earth model with continuous stratification, finite compressibility and self-gravitation. Here, an optimized method to

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33

Ranjit, Dhunde, and Dhongle Prashant. "Solving Two-Dimensional Helmholtz and Poisson Equations Using Double Laplace Transform Method." Indian Journal of Science and Technology 18, no. 12 (2025): 962–68. https://doi.org/10.17485/IJST/v18i12.3705.

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Abstract <strong>Objectives:</strong> To explore the efficacy of the double Laplace transform technique in solving 2D Helmholtz and Poisson equations. <strong>Methods:</strong> The double Laplace transform clearly converts the 2D Helmholtz and Poisson equations into an algebraic calculation in the Laplace domain that can be solved easily. <strong>Findings:</strong> The double Laplace transform method offers exact solutions to the Helmholtz and Poisson equations by resolving a series of specific and understandable examples. <strong>Novelty:</strong> This resea

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34

Ohshima, Hiroyuki. "Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle." Molecules 27, no. 16 (2022): 5108. http://dx.doi.org/10.3390/molecules27165108.

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The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general

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35

Wang, Jian, Kamran, Ayesha Jamal, and Xuemei Li. "Numerical Solution of Fractional-Order Fredholm Integrodifferential Equation in the Sense of Atangana–Baleanu Derivative." Mathematical Problems in Engineering 2021 (February 12, 2021): 1–8. http://dx.doi.org/10.1155/2021/6662808.

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In the present article, our aim is to approximate the solution of Fredholm-type integrodifferential equation with Atangana–Baleanu fractional derivative in Caputo sense. For this, we propose a method based on Laplace transform and inverse LT. In our numerical scheme, the given equation is transformed to an algebraic equation by employing the Laplace transform. The reduced equation will be solved in complex plane. Finally, the solution of the given problem is obtained via inverse Laplace transform by representing it as a contour integral. Then, the trapezoidal rule is used to approximate the in

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Al-Omari, Shrideh Khalaf Qasem. "On a class of generalized Meijer–Laplace transforms of Fox function type kernels and their extension to a class of Boehmians." Georgian Mathematical Journal 25, no. 1 (2018): 1–8. http://dx.doi.org/10.1515/gmj-2016-0056.

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AbstractIn this paper, we investigate a Meijer–Laplace transform enfolding Fox’sH-functions on a class of Boehmians. The extended Meijer–Laplace transform of a Boehmian is determined and executed to preserve certain properties of the classical transform. The inverse problem and related theorems are also discussed in some details.

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37

Muzychuk, A. O. "The Laguerre transform of a convolution product of vector-valued functions." Matematychni Studii 55, no. 2 (2021): 146–61. http://dx.doi.org/10.30970/ms.55.2.146-161.

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The Laguerre transform is applied to the convolution product of functions of a real argument (over the time axis) with values in Hilbert spaces. The main results have been obtained by establishing a relationship between the Laguerre and Laplace transforms over the time variable with respect to the elements of Lebesgue weight spaces. This relationship is built using a special generating function. The obtained dependence makes it possible to extend the known properties of the Laplace transform to the case of the Laguerre transform. In particular, this approach concerns the transform of a convolu

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Dmytryshyn, M. I. "Approximation by interpolation spectral subspaces of operators with discrete spectrum." Matematychni Studii 55, no. 2 (2021): 162–70. http://dx.doi.org/10.30970/ms.55.2.162-170.

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The Laguerre transform is applied to the convolution product of functions of a real argument (over the time axis) with values in Hilbert spaces. The main results have been obtained by establishing a relationship between the Laguerre and Laplace transforms over the time variable with respect to the elements of Lebesgue weight spaces. This relationship is built using a special generating function. The obtained dependence makes it possible to extend the known properties of the Laplace transform to the case of the Laguerre transform. In particular, this approach concerns the transform of a convolu

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39

Sanusi, Wahidah, Syafruddin Side, and Beby Fitriani. "Solusi Persamaan Transport dengan Menggunakan Metode Dekomposisi Adomian Laplace." Journal of Mathematics, Computations, and Statistics 2, no. 2 (2020): 173. http://dx.doi.org/10.35580/jmathcos.v2i2.12580.

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Abstrak. Penelitian ini mengkaji terbentuknya persamaan Transport dan menerapkan metode Dekomposisi Adomian Laplace dalam menentukan solusi persamaan Transport. Persamaan transport merupakan salah satu bentuk dari persamaan diferensial parsial. Bentuk umum persamaan Transport yaitu: Metode Dekomposisi Adomian Laplace merupakan kombinasi antara dua metode yaitu metode dekomposisi adomian dan transformasi laplace. Penyelesaian persamaan Transport dengan metode Dekomposisi Adomian Laplace dilakukan dengan cara menggunakan tranformasi Laplace, mensubstitusi nilai awal, menyatakan solusi dalam bent

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40

Akram, Zaryab. "Cryptology Based on Laplace Transform of Hyperbolic Function and Matrix Decomposition Method." ECS Meeting Abstracts MA2022-02, no. 64 (2022): 2364. http://dx.doi.org/10.1149/ma2022-02642364mtgabs.

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Cryptography is the art of coding and decoding the communication. Cryptography ensures the security of delicate information over some confidentiality breaching resources. In the recent age Cryptography has turned into a battleground of some of the world’s best mathematicians and computer scientists. A number of transforms like Sumudu transform, Laplace transform, Fourier transform, Kamal transform, Mellin transform, Jafari transform, Aboodh transform, N-transform, ELzaki transform, MAHGOUB transform are frequently used in cryptography. Cryptography is of great importance in every field of life

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Luo, Shuang, and Fu-yao Zhao. "A Semi-Analytical Solution of Inverse Laplace Transform." Journal of Mathematics 2022 (August 19, 2022): 1–6. http://dx.doi.org/10.1155/2022/9129727.

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We propose a general method for constructing the semi-analytical solution of the inverse Laplace transform, realized through the powerful exponential approximation invented by Wang et al. in 1993. Bearing their credits, this method inherits all the merits such as analytical expression, avoiding free parameters, simple calculation with high accuracy, and the availability of error estimation. Illustrating calculations indicate the potential applications to the vast problems in the fields of mathematical physics as well as engineering and medicine.

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Ghiya, Neeti, K. Sridevi, and S. Manjula. "Inverse Laplace Transform of the Incomplete H-Function." ECS Transactions 107, no. 1 (2022): 11179–88. http://dx.doi.org/10.1149/10701.11179ecst.

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Special functions have enormous applications in theoretical and applied mathematics. This field is constantly expanding and addressing new problems in engineering applications and applied sciences. H-function one and more variables have been applied in large range of areas, such as electronics and communication, astrophysics, fractional differential equations, super statistics, diffusion, reaction–diffusion, and other fields like probability theory, biology, and theoretical physics. Some situations of heat conduction and astrophysics problems are not adequately addressed by basic category of s

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43

Shibuya, Kengo, Haruo Saito, Hideaki Tashima, and Taiga Yamaya. "Using inverse Laplace transform in positronium lifetime imaging." Physics in Medicine & Biology 67, no. 2 (2022): 025009. http://dx.doi.org/10.1088/1361-6560/ac499b.

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Abstract Positronium (Ps) lifetime imaging is gaining attention to bring out additional biomedical information from positron emission tomography (PET). The lifetime of Ps in vivo can change depending on the physical and chemical environments related to some diseases. Due to the limited sensitivity, Ps lifetime imaging may require merging some voxels for statistical accuracy. This paper presents a method for separating the lifetime components in the voxel to avoid information loss due to averaging. The mathematics for this separation is the inverse Laplace transform (ILT), and the authors exami

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Guglielmi, Nicola, María López-Fernández, and Giancarlo Nino. "Numerical inverse Laplace transform for convection-diffusion equations." Mathematics of Computation 89, no. 323 (2020): 1161–91. http://dx.doi.org/10.1090/mcom/3497.

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LlOU, CHING-TIEN, and YI-SHYONG CHOU. "Inverse Laplace transform by piecewise linear polynomial functions." International Journal of Systems Science 18, no. 4 (1987): 749–54. http://dx.doi.org/10.1080/00207728708964006.

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YAMAOKA, Kiyoshi. "Disposition Analysis by Fast Inverse Laplace Transform (FILT)." YAKUGAKU ZASSHI 112, no. 8 (1992): 503–15. http://dx.doi.org/10.1248/yakushi1947.112.8_503.

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Rani, Dimple, Vinod Mishra, and Carlo Cattani. "Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations." Symmetry 11, no. 4 (2019): 530. http://dx.doi.org/10.3390/sym11040530.

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This paper discusses the applications of numerical inversion of the Laplace transform method based on the Bernstein operational matrix to find the solution to a class of fractional differential equations. By the use of Laplace transform, fractional differential equations are firstly converted to system of algebraic equations then the numerical inverse of a Laplace transform is adopted to find the unknown function in the equation by expanding it in a Bernstein series. The advantages and computational implications of the proposed technique are discussed and verified in some numerical examples by

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Li, Jianhui, Colin G. Farquharson, and Xiangyun Hu. "Three effective inverse Laplace transform algorithms for computing time-domain electromagnetic responses." GEOPHYSICS 81, no. 2 (2016): E113—E128. http://dx.doi.org/10.1190/geo2015-0174.1.

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The inverse Laplace transform is one of the methods used to obtain time-domain electromagnetic (EM) responses in geophysics. The Gaver-Stehfest algorithm has so far been the most popular technique to compute the Laplace transform in the context of transient electromagnetics. However, the accuracy of the Gaver-Stehfest algorithm, even when using double-precision arithmetic, is relatively low at late times due to round-off errors. To overcome this issue, we have applied variable-precision arithmetic in the MATLAB computing environment to an implementation of the Gaver-Stehfest algorithm. This ap

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Khalouta, Ali. "A new exponential type Kernel integral transform: Khalouta transform and its applications." Mathematica Montisnigri 57 (2023): 5–23. http://dx.doi.org/10.20948/mathmontis-2023-57-1.

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In this paper, we suggest a new integral transform called the Khalouta transform, which is a generalization of many integral transforms having exponential type kernel. We discuss certain results on the inverse and the existence of this integral transform. We present useful properties of the Khalouta transform and their applications to solve differential equations. Furthermore, we prove the duality between the Khalouta transform and other transforms such as the Laplace-Carson transform, Sumudu transform, ZZ transform, ZMA transform, Elzaki transform, Aboodh transform, Natural transform and Sheh

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Hidan, Muajebah, Salah Mahmoud Boulaaras, Bahri-Belkacem Cherif, and Mohamed Abdalla. "Further Results on the p , k − Analogue of Hypergeometric Functions Associated with Fractional Calculus Operators." Mathematical Problems in Engineering 2021 (March 30, 2021): 1–10. http://dx.doi.org/10.1155/2021/5535962.

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In a previous article, first and last researchers introduced an extension of the hypergeometric functions which is called “ p , k -extended hypergeometric functions.” Motivated by this work, here, we derive several novel properties for these functions, including integral representations, derivative formula, k-Beta transform, Laplace and inverse Laplace transforms, and operators of fractional calculus. Relevant connections of some of the discussed results here with those presented in earlier references are outlined.

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