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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 635690, 4 pages
Research Article

-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over -Adic Fields

Department of Applied Mathematics, Nanjing University of Finance & Economics, Nanjing 210023, China

Received 23 April 2013; Accepted 13 June 2013

Academic Editor: Thabet Abdeljawad

Copyright © 2013 Bo Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we study the solutions of the pseudodifferential equations of type over -adic field , where is a -adic fractional pseudodifferential operator. If is a Bruhat-Schwartz function, then there exists a distribution , a fundamental solution, such that is a solution. We also show that the solution belongs to a certain Sobolev space. Furthermore, we give conditions for the continuity and uniqueness of .