The Laplace Transform Method for the Analysis of Continuous Time Signals and Systems

A relatively new iterative Laplace transform method, which combines two methods; the iterative method and the Laplace transform method, is applied to obtain the numerical solutions of fractional Fokker-Planck equations. The method gives numerical solutions in the form of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and straightforward when applied to space-time fractional Fokker-Planck equations. The method provides a promising tool for solving space-time fractional partial differential equations.

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Exact solution of time-fractional partial differential equations using Laplace transform

International Journal of Basic and Applied Sciences ◽

10.14419/ijbas.v5i1.5665 ◽

2016 ◽

Vol 5 (1) ◽

pp. 86

Author(s):

Naser Al-Qutaifi

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Laplace Transform ◽

Fractional Partial Differential Equations ◽

Laplace Transform Method ◽

Partial Differential ◽

Transform Method ◽

Integer Order ◽

First Derivative ◽

The Laplace Transform

<p>The idea of replacing the first derivative in time by a fractional derivative of order , where , leads to a fractional generalization of any partial differential equations of integer order. In this paper, we obtain a relationship between the solution of the integer order equation and the solution of its fractional extension by using the Laplace transform method.</p>

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Aeroelastic Flutter of Continuous Systems: A Generalized Laplace Transform Method

Journal of Applied Mechanics ◽

10.1115/1.4033597 ◽

2016 ◽

Vol 83 (8) ◽

Cited By ~ 3

Author(s):

Arion Pons ◽

Stefanie Gutschmidt

Keyword(s):

Laplace Transform ◽

Continuous Systems ◽

Laplace Transform Method ◽

Aeroelastic System ◽

Transform Method ◽

Wing Model ◽

System A ◽

Aeroelastic Flutter ◽

The Laplace Transform ◽

Eigenvalue Parameter

This paper presents a generalization of the Laplace transform method (LTM) for determining the flutter points of a linear ordinary-differential aeroelastic system—a linear system involving a spatial derivative as well as a time-eigenvalue parameter. Current implementations of the LTM have two major problems: they are unable to solve systems of arbitrary size, order, and boundary conditions, and they require certain key operations to be performed by hand or with symbolic manipulation libraries. Our generalized method overcomes both these problems. We also devise a new method for solving and visualizing the algebraic system that arises from the LTM procedure. We validate our generalized LTM and novel solution method against both the Goland wing model and a large system of high differential order, as a demonstration of their effectiveness for solving such systems.

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