TITLE: What is the intuitive or geometric explaination of fractional derivatives?
QUESTION [6 upvotes]: I'm starting to study more advanced solid mechanics, particularly understanding elastomers' stress strain relationships and creep. A common way of describing the variation in the aforementioned relationship as the material is cycled to describe energy loss due to entropy change and this is mathematically described using fractional derivatives.
Is there an intuitive description for a fractional derivative? To use extremely simple calculus examples, by intuitive, I mean the way derivatives are described as rates of change of one variable with respect to another and integrals are described as net change. Or a geometric interpretation such as slopes of lines and areas under curves.

REPLY [2 votes]: Relevant information about the geometric interpretation of fractional derivatives can be found in those papers :
http://www.mathem.pub.ro/dgds/v15/D15-ta.pdf
http://www.scielo.org.mx/pdf/rmf/v60n1/v60n1a6.pdf
http://www.gauge-institute.org/calculus/FractionalCalculus.pdf
http://www.rxiv.org/pdf/1206.0005v1.pdf
Intuitive interpretation in physic, in case of MIXED phenomena which models are some functions, classical derivatives and/or classical antiderivatives of them. This leads to a common behaviour represented by fractional derivatives. A clear example can be shown in electrical impedance analysis : Next Table comes from 
http://fr.scribd.com/doc/14686539/The-Fractional-Derivation-La-derivation-fractionnaire

Some models for mixed electrical phenomena are discussed in the paper :
http://fr.scribd.com/doc/71923015/The-Phasance-Concept