Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractio...

The aim of the present paper is to obtain certain new integral inequalities involving the Saigo fractional integral operator. It is also shown how the various inequalities considered in this paper admit themselves of q -extensions which are capable of yielding various results in the theory of q -integral inequalities. Mathematics subject classification (2010): 26D10, 26A33, 05A30.

Fractal and Fractional are two words referring to some characteristics and fundamental problems which arise in all fields of science and technology. These problems are characterized by having some non-integer order features. Fractals are geometrical objects with non-integer dimension, while fractional is the non-integer order of differential operators. Fractals and fractional calculus have been...

Exploring the possible links between the mathematical field of fractional calculus and the electromagnetic theory has been one of the topics of our research interests in recent years. We have studied the possibility of bringing the tools of fractional calculus and electromagnetic theory together, and have explored and developed the topic of fractional paradigm in electromagnetic theory (see e.g...

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of VolterraFredholm type differential equations with nonlocal conditions in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. MSC: 34K37 • 34A08 • 47H10