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...

Abstract In this paper, an exact analytical solution for the motion of fractionalized second grade fluid flows moving over accelerating plate under influence slip has been obtained. A coupled system partial differential equations representing equation re-written in terms fractional derivatives form by using Caputo operator. The Discrete Laplace transform method employed computing expressions ve...

Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing extended Pochhammer symbol. First, and express certain integral equations differential formulae concerning it. We also Mellin transform function. After that, some fractional calculus findings for these expanded functions. Lastly, several theorems in Kinetic equations.

The fundamental set of solutions of the generalized hypergeometric differential equation in the neighborhood of unity has been built by Nørlund in 1955. The behavior of the generalized hypergeometric function in the neighborhood of unity has been described in the beginning of 1990s by Bühring, Srivastava and Saigo. In the first part of this paper we review their results rewriting them in terms ...

Abstract The compounded Bell generalized class of distributions is proposed in this article as an alternative to the Poisson family distributions. Some properties and actuarial measures are presented. a special model named Weibull (BellW) obtained such linear representation density, r th moment, incomplete moment generating function using Wright hypergeometric Meijer’s G function, p order stati...

We establish two binomial coefficient–generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of the author, they are used to establish modulo p (k > 1) congruences between truncated generalized hypergeometric series, and a function which extends Greene’s ...

Through this article, we will discuss a new extension of the incomplete Wright hypergeometric matrix function by using extended Pochhammer symbol. First, give generalization and state some integral equations differential formulas about it. Next, obtain results fractional calculus these functions. Finally, an application in kinetic equations.

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeomet-ric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E 7 (ellip-tic, hyperbolic) and of type E 6...