A perturbative study of fractional relaxation phenomena

作者：Tofighi A^*; Golestani A

来源：Physica A: Statistical Mechanics and Its Applications , 2008, 387(8-9): 1807-1817.

DOI：10.1016/j.physa.2007.11.046

• fractional equations
• fractional relaxation

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.

• 出版日期2008-3-15