A perturbative study of fractional relaxation phenomena

摘要

Fractional differential equations provide a convenient mathematical framework to discuss many important physical processes in the complex media. An expansion method has been proposed [V.E. Tarasov, G.M. Zaslavsky, Physica A 368 (2006) 399-415] to discuss the dynamics in the media where the order of the fractional derivative alpha is close to an integer number. This expansion is over the small parameter epsilon = n - alpha with small positive E and positive integer n. They also found that this expansion in not uniform with respect to I 1. We extend the formalism to the values of alpha = n + epsilon. we also show that in certain cases this expansion is uniform. We apply this uniform expansion to the fractional relaxation, composite fractional relaxation and to the composite fractional oscillation phenomena. (c) 2007 Elsevier B.V. All rights reserved.