Cosmology under the fractional calculus approach

Lens spaces in the Regge calculus approach to quantum cosmology.

Cobordism Effects in the Regge Calculus Approach to Quantum Cosmology

We study the ground state wave function for a universe which is topologically a lens space within the Regge calculus approach. By restricting the four dimensional simplicial complex to be a cone over the boundary lens space, described by a single internal edge length, and a single boundary edge length, one can analyze in detail the analytic properties of the action in the space of complex edge ...

Matrix Approach to Discrete Fractional Calculus

A matrix form representation of discrete analogues of various forms of fractional differentiation and fractional integration is suggested. The approach, which is described in this paper, unifies the numerical differentiation of integer order and the n-fold integration, using the so-called triangular strip matrices. Applied to numerical solution of differential equations, it also unifies the sol...

A Fractional Calculus Approach to the Mechanics of Fractal Media

Based on the experimental observation of the size effects on the structural behavior of heterogeneous material specimens, the fractal features of the microstructure of such materials is rationally described. Once the fractal geometry of the microstructure is set, we can define the quantities characterizing the failure process of a disordered material (i.e. a fractal medium). These quantities sh...

On certain fractional calculus operators involving generalized Mittag-Leffler function

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...