The first topic is Fractional calculus with applications in probability and stochastic processes.
After an introduction to Fractional calculus ,complex Mellin transform is defined.It is shown that Mellin transform is related to Riesz operators in zero.
With these concepts in mind a new representation of the probability density function and the power spectral density function of stochastic processes is presented.Then it is shown that with a limited number of complex moments the probability density function and the power spectral density may be easiliy reconstructed in the domains including the trend at infinity.
The second topic is Fractional viscoelasticity.
From the Creep experimental tests performed on real materials it is widely recognized that the consequent strain -time curve is well fitted by a power law.By using Boltzmann superposition principle with power law kernel a fractional constitutive law comes out in a natural way.It follows that the stress strain relation of viscoelastic material is ruled by a fractional differential equation.
Mechanical interpretation of such fractional differerential equation is discussed in detail.
