We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on particular yet relevant case, for which provide several ready-for-use combinatorial identities, including an adapted version the Pascal's rule. then investigate associated generating functions, establish recursive, and integral formulation. From this, derive asym...

The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiat...

Fractional differential calculus have recently been addressed by many researchers of various fields of science and engineering such as physics, chemistry, biology, economics, control theory, and biophysics, etc. [1-4]. In particular, the existence of solutions to fractional boundary value problems is under strong research recently, see [5-7] and references therein. The fractional q-difference c...

In this paper, a new theory of generalized micropolar thermoelasticity is derived by using fractional calculus. The generalized heat conduction equation in micropolar thermoelasticity has been modified with two distinct temperatures, conductive temperature and thermodynamic temperature by fractional calculus which depends upon the idea of the RiemannLiouville fractional integral operators. A un...

Series expansion methods for fractional integrals are important and useful for treating certain problems of pure and applied mathematics. The aim of the present investigation is to obtain certain new fractional calculus formulae, which involve Srivastava polynomials. Several special cases of our main findings which are also believed to be new have been given. For the sake of illustration, we po...

We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection–dispersion equation for flow in heterogeneous porous media. r 2005 Elsevier B.V. All rights reserved.

The sets and curves of fractional dimension have been constructed and found to be useful at number of places in science [1]. They are used to model various irregular phenomena. It is wellknown that the usual calculus is inadequate to handle such structures and processes. Therefore a new calculus should be developed which incorporates fractals naturally. Fractional calculus, which is a branch of...

Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes type present biological systems, can be treated by fractional calculus. We also analyse contribution historical values function evaluation operators accor...