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The accurate numerical inversion of laplace transforms [PDF]
, 1976 Inversion of almost arbitrary Laplace transforms is effected by trapezoidal integration along a special contour. The number n of points to be used is one of several parameters, in most cases yielding absolute errors of order 10-7 for n = 10, 10-11 for n
Tablot, A
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Laplace transform of fractional order differential equations
Electronic Journal of Differential Equations, 2015 In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform.
Song Liang, Ranchao Wu, Liping Chen
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Lossy transmission line response via numerical Laplace transform inversion [PDF]
, 1994 An efficient transient analysis of lossy lines with nonlinear loads requires the ability to compute and represent a suitable set of line impulse responses.
F.G. Canavero +3 more
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Results in Physics, 2023 Differential equations involving fractional order operators appear frequently in various research areas. Solving a differential equation containing a fractional derivative is very difficult.
Kamran +4 more
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Journal of the Australian Mathematical Society, 1971 In this paper we suppose that the function s(x) is integrable in the Lebesgue sense for every finite interval of x ≥ 0. If exists, we say that the integral exists.
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The h-Laplace and q-Laplace transforms
Journal of Mathematical Analysis and Applications, 2010 For a given function \(x\) with complex values the \(h\)-Laplace transform is defined as \[ (h/(1+hz))\sum^\infty_{k=0}x(kh)/(1+ hz)^k, \] and the \(q\)-Laplace transform as \[ (q-1)\sum^\infty_{n=0} q^nx(q^n)/\prod^n_{k=0} (1+(q- 1)q^k z), \] where \(z\) is the complex variable in the image domain.
Bohner, Martin, Guseinov, Gusein Sh.
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On Non Conformable Fractional Laplace Transform [PDF]
, 2021 In the present paper, the main theorems of the classical Laplace transform are generalized in the non-conforming Laplace transform with nucleus et−α .
E. Na ́poles Valde ́s, Juan +4 more
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On the Laplace Transform of the Lognormal Distribution [PDF]
Methodology and Computing in Applied Probability, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Asmussen, Søren +2 more
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, 2022 : Based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, this paper provides several examples to illustrate how to use fractional Laplace transform to find the solution of linear system of fractional differential equations.
Chii-Huei Yu
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On q-double modified Laplace transform [PDF]
Mathematics and Computational SciencesThe Laplace transform is widely used in science and technology to deal with complex problemsin stability and control systems. The modified Laplace transform has been applied in physics andmathematics to solve boundary layer equations in ordinary ...
Srikumar Panda +2 more
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