Mridula Garg

Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions

The main object of this paper is to further investigate the generalized Apostol–Bernoulli polynomials of higher order, which were introduced and studied recently by Luo and Srivastava [2005, Journal of Mathematical Analysis and Applications, 308, 290–302; 2006, Computers and Mathematics with Applications, 51, 631–642]. Here, we first derive an explicit representation of these generalized Apostol–Bernoulli polynomials of higher order in terms of a generalization of the Hurwitz–Lerch Zeta function and then proceed to establish a functional relationship between the generalized Apostol–Bernoulli polynomials of rational arguments and the Hurwitz (or generalized) Zeta function. Our results would provide extensions of those given earlier by (for example) Apostol [1951, Pacific Journal of Mathematics, 1, 161–167] and Srivastava [2000, Mathematical Proceedings of the Cambridge Philosophical Society, 129, 77–84].

A new generalization of the Bernoulli and related polynomials

A class of solutions, decaying as

On a generalized finite Hankel transform

t\rightarrow \infty

Generalized Differential Transform Method to Space-Time Fractional Telegraph Equation

, of a two-dimensional model problem on the oscillations of an ideal rotating fluid in some domains with angular points is constructed explicitly. The existence of solutions whose

On Distribution of Order Statistics from Kumaraswamy Distribution

L_2

On a new unified integral

-norms decrease more rapidly than any negative power of

Study of a class of generalized elliptic type integrals

t

The distribution of the product of two independent generalized trapezoidal random variables

, is established.In this paper, we introduce and investigate a generalization of the Bernoulli polynomials by means of a suitable generating function. We establish several interesting properties of these general polynomials. Furthermore, we give explicit series representations for these general polynomials in terms of a certain generalized Hurwitz-Lerch zeta function and the familiar Gauss hypergeometric function.

Generalisation of Taylor's Formula and Differential Transform Method for Composite Fractional Derivative

In the present work we introduce a finite integral transform involving combination of Bessel functions as kernel under prescribed conditions. The corresponding inversion formula and some properties of this transform have also been given. Three problems of heat conduction in an infinite, a semi-infinite and a finite circular cylinder bounded by given surfaces with radiation-type boundary value conditions have been solved by applying this transform.

A Mittag-Leffler-type function of two variables

We use generalized differential transform method (GDTM) to derive the solution of space-time fractional telegraph equation in closed form. The space and time fractional derivatives are considered in Caputo sense and the solution is obtained in terms of Mittag-Leffler functions.