On a Riemann-Liouville fractional analog of the Laplace operator with positive energy

• Type: Article in International Scientific Journal
• Date: 2012

Authors

Dalla D Riva (Author) Other; Yakubovich, S (Author) FCUP

Journal

Title: Integral Transforms and Special Functions

Vol. 23

Pages: 277-295

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 10 Citations

Scopus - 10 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-002-GRR

DOI: 10.1080/10652469.2011.576832

Abstract (EN): The purpose of this paper is to define a particular fractional analog of the Laplace operator in a rectangular domain in the plane by exploiting the Riemann-Liouville fractional derivatives. Such a definition allows the introduction of fractional boundary value problems which correspond to the classical Dirichlet, Neumann and mixed boundary value problems for the Laplace operator. By exploiting a suitable Integration by Parts Formula and the positiveness of the corresponding energy integral, we verify some uniqueness results for the solutions of the boundary value problems and show the existence of particular solutions.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19