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23 April 2024

» arxiv » 1905.3343

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An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution
Fernando Olivar-Romero ; Oscar Rosas-Ortiz ;
Date:	8 May 2019
Abstract:	We solve the Cauchy problem defined by the fractional partial differential equation $[partial_{tt}-kappamathbb{D}]u=0$, with $mathbb{D}$ the pseudo-differential Riesz operator of first order, and the initial conditions $u(x,0)=mu(sqrt{pi}x_0)^{-1}e^{-(x/x_0)^2}$, $u_t(x,0)=0$. The solution of the Cauchy problem resulting from the substitution of the Gaussian pulse $u(x,0)$ by the Dirac delta distribution $varphi(x)=mudelta(x)$ is obtained as corollary.
Source:	arXiv, 1905.3343
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