Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 3, Pages 197-211

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

Copyright © 2004 Mahmoud M. El-Borai. 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.


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.