Fractional calculus

With the help of fractional calculus, Dassas and Duby123 have worked on the problem of diffusion towards the fractal interfaces. They have proposed the following generalized diffusion equation involving a fractional derivative operator ... 

K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, London, 1974. 

Refs. [i] Oldham KB, Spanier / (2006) The fractional calculus. Dover, New York [ii] Oldham KB (1997) / Electroanal Chem 430 3... 

Application of Fractional Calculus in Physics, R. Hilfer, ed., World Scientific, Singapore, 2000. 

K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley Sons, New York, 1993. 

How general are our results From a stochastic point of view ergodicity breaking, Levy statistics, anomalous diffusion, aging, and fractional calculus, are all related. In particular ergodicity breaking is found in other models with power-law distributions, related to the underlying stochastic model (the Levy walk). For example, the well known continuous time random walk model also... 

In Ref. 65 the conjecture was made that the emergence at macroscopic level of processes requiring fractional calculus is the consequence of infinitely extended memory breaking the separation between microscopic dynamics, supposed to be not continuous and not differentiable. The same conjecture has... 

FRACTAL PHYSIOLOGY, COMPLEXITY, AND THE FRACTIONAL CALCULUS 49 some algebra... 

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