Fractional calculus operators and their applications to thermal systems

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...

Notes on Some Fractional Calculus Operators and Their Properties

Here we state the main properties of the Caputo, Riemann-Liouville and the Caputo via Riemann-Liouville fractional derivatives and give some general notes on these properties. Some properties given in some recent literatures and used to solve fractional nonlinear partial differential equations will be proved that they are incorrect by giving some counter examples.

Analytic function theory, fractional calculus and their applications

Fractional calculus and its applications.

Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, etc. [1,2]. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. It has been found that fraction...

q-ANALOGUES OF SAIGO’S FRACTIONAL CALCULUS OPERATORS

M. Saigo [Math. Rep. Coll. Gen. Educ., Kyushu Univ., 11 (1978) 135-143] has defined a pair of fractional integral operators and fractional derivatives involving generalizd hypergeometric function. The aim of present paper is to define their q-analogues. First, we define a pair of q-analogues of Saigo’s fractional integral operators and establish some results for it. Next, we define a pair of q-...