Fractional differential equations as alternative models to nonlinear differential equations. (English) Zbl 1120.34323

Summary: The main objective of this paper is to demonstrate the possibility of using fractional differential equations to simulate the dynamics of anomalous processes whose analytical representations are continuous but strongly not differentiable, like Weierstrass-type functions. This allows for the possibility of modeling phenomena which traditional differential modeling cannot accomplish. To this end we shall see how some functions of this kind have a fractional derivative at every point in a real interval, and are therefore solutions to fractional differential equations.


34C60 Qualitative investigation and simulation of ordinary differential equation models
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