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

In this paper, we study the solutions of the pseudodifferential equations of type D(alpha)u = v over p-adic field Q(p), where D-alpha is a p-adic fractional pseudodifferential operator. If V is a Bruhat- Schwartz function, then there exists a distribution E-alpha, a fundamental solution, such that u = E-alpha * v 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 u.