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In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
An integral transform denoted by that generalizes the well-known Laplace and Meijer transformations, is studied in this paper on certain spaces of generalized functions introduced by A.C. McBride by employing the adjoint method.
We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for the vibration...
2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10,
45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation
processes governed by linear differential equations of fractional order. The
fractional derivatives are intended both in the Rieamann-Liouville sense
and in the Caputo sense. After giving a necessary outline of the classica
theory of linear viscoelasticity, we contrast these two types of fractiona
derivatives in their ability to take into...
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