Fractional behaviour of partial differential equations whose coefficients are exponential functions of the space variable

Abstract

There exists a close link between fractional systems and infinite dimensional systems described by diffusion equations. This link can be demonstrated analytically and is reminded in this article. This fractional behaviour results in fact in the system infinite dimension along with constant geometric characteristics. This article demonstrates that several other classes of differential equations also exhibit, on a frequency band, a fractional behaviour. The fractional behaviour is obtained with these equations on a space of finite dimension but with particular geometric characteristics.