Journal of Applied Mathematics and Stochastic Analysis 
Volume 2004 (2004), Issue 3, Pages 197-211
doi:10.1155/S1048953304311020

The fundamental solutions for fractional evolution equations of parabolic type

Mahmoud M. El-Borai

 Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
Received 19 November 2003; Revised 22 May 2004

Abstract

The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.