The theory of fractional calculus goes back to the beginning of the theory of di erential calculus but its inherent complexity postponed the application of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of a...

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 operat...

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The...