Fundamental solutions of the fractional Fresnel equation in the real half-line

M.A. Taneco-Hernández, V.F. Morales-Delgado and J.F. Gómez-Aguilar

Physica A: Statistical Mechanics and its Applications, 2019, vol. 521, issue C, 807-827

Abstract: The purpose of this paper is to offer a discussion on the fundamental solutions for the vibration fractional equation of rods semi-infinite (also called Fresnel equation). For this end, using the fractional derivative of Riemann–Liouville of order γ∈(1,2] with respect to the spatial variable, we solve boundary-value problems associated to the mentioned equation showing the connection with Brownian behavior and the heat equation. We obtain solutions for the fractional Fresnel equation using the unified transform method. In the intermediate of the investigation, we have solved generalized Cauchy problems associated with linear fractional Schrödinger equations with order γ.

Keywords: Fractional Fresnel equation; Generalized Cauchy problems; Unified transform method; Fundamental solutions (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:521:y:2019:i:c:p:807-827

DOI: 10.1016/j.physa.2019.01.105

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