Jyotindra C. Prajapati

SOME REMARKS ON GENERALIZED MITTAG-LEFFLER FUNCTION

The principal aim of the paper is to establish the function and its properties by using Fractional Calculus. We also obtained some integral representations of the function which is recently introduced by Shukla and Prajapati[6].

ON SOME PROPERTIES OF A CLASS OF POLYNOMIALS SUGGESTED BY MITTAL

The object of this paper is to establish some generating relations by using operational formulae for a class of polynomials T (α+s−1) kn (x) defined by Mittal. We have also derived finite summation formulae for (1.6) by employing operational techniques. In the end several special cases are discussed.

A general class of polynomials associated with generalized Mittag–Leffler function

Several authors have defined polynomial sets by means of general Rodrigues formulae in different forms. In this article, an attempt is made to provide an elegant unification of several classes of polynomials. We investigate a general class of polynomials by means of a generalized Rodrigues formula defined as (2) associated with a generalized Mittag–Leffler function , which is recently introduced by Shukla and Prajapati [Shukla, A.K. and Prajapati, J.C., On a generalisation of Mittag–Leffler function and its properties. Journal of Mathematical Analysis and Appplications, article in press]. We have also derived several families of generating relations, finite summation formulae for equation (2) by employing operational techniques and bilateral-generating relation. In the end, several special cases have been discussed.

SOME PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTION

In present paper, we obtain functions R t(c,�,a,b) and R t(c, µ,a,b) by using generalized hypergeometric function. A recurrence re- lation, integral representation of the generalized hypergeometric function 2R1(a,b;c;� ;z) and some special cases have also been discussed.

On the Laguerre transform in two variables

The main objective of the present article is to introduce the Laguerre transform of two variables. We obtained some basic operational properties and also examined the MAPLE implementation to obtain the aforementioned transform.

GENERALIZATION OF A CLASS OF POLYNOMIALS

In [1], R. Andre-Jeannin considered a class of polynomials Un(p, q; x) defined by Un(P> ft ) = ( + P)U„-i(P, ft ) ~ qUn-iiP, ft x), n>\9 with initial values U0(p, q;x) = 0 and U{(p, q;x) = l. Particular cases of Un(p,q;x) are: the well-known Fibonacci polynomials Fn(x); the Pell polynomials Pn(x) (see [4]); the Fermat polynomials of the first kind fl(x) (see [5], [3]); and the Morgan-Voyce polynomials of the second kind Bn(x) (see [2]). In this paper we shall consider the polynomials

ON SEQUENCE OF FUNCTIONS

„(p, q; x) defined by

Functions of bounded fractional differential variation – A new concept

Operational techniques have drawn the attention of several researchers in the study of sequence of functions and polynomials. An attempt is made to introduce a new sequence of functions by using op- erational techniques. Some generating relations and finite summation formulae have been obtained. The corresponding MAPLE code for ob- taining above sequence of functions for different values of parameters was also discussed.

On a generalization of Mittag-Leffler function and its properties

Abstract The idea of functions of bounded differential variation was introduced by Bhatt, Dabhi and Kachhia in [2]. In the present paper, we introduce functions of bounded fractional differential variation using the Caputo-type fractional derivative instead of the commonly used first-order derivative. Various properties and relation with some known results of classical analysis are also studied. We prove that the space BFDV ⁢ [ a , b ]

ON A RECURRENCE RELATION OF GENERALIZED MITTAG-LEFFLER FUNCTION

{\mathrm{BFDV}[a,b]}