Unique continuation principle for the one-dimensional time-fractional diffusion equation

This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order α (0, 1). Firstly, the uniqueness of solutions to a lateral Cauchy problem for the anomalous diffusion equation is given via the Theta function method, from which we further verify the unique continuation principle. © 2019 Diogenes Co., Sofia.

Authors
Li Z. 1 , Yamamoto M. 2, 3, 4
Journal
Fractional Calculus and Applied Analysis
Publisher
Walter de Gruyter GmbH
Issue number
3
Language
English
Pages
644-657
State
Published
Link
External link
DOI
10.1515/FCA-2019-0036
Volume
22
Year
2019
Organizations
  • 1 School of Mathematics and Statistics, Shandong University of Technology, No. 266, Xincunxi Road, Zhangdian District Zibo, Shandong, 255049, China
  • 2 Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
  • 3 Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow, 117198, Russian Federation
  • 4 Honorary Member of Academy of Romanian Scientists, Splaiul Independentei Str. no 54, Bucharest, 050094, Romania
Keywords
Fractional diffusion equation; fractional Theta function; Laplace transform; unique continuation principle
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