Pratibha Manohar

Generalized Differential Transform Method to Space-Time Fractional Telegraph Equation

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.

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

ABSTRACT In this article, we derive the probability density function (pdf) of the product of two independent generalized trapezoidal random variables having different supports, in closed form, by considering all possible cases. We also show that the results for the product of two triangular and uniform random variables follow as special cases of our main result. As an illustration, we obtain pdf of product for a suitably constrained set of parameters and plot some graphs using MATLAB, which express variation in pdf with change in different parameters of the generalized trapezoidal distribution.

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

In this paper, we first establish a generalized Taylors formula for composite fractional derivative and then develop the generalized differential transform method for composite fractional derivative. As an application, we solve fractional Fokker–Planck Equation (FFPE) with space derivative considered as composite fractional derivative and time derivative considered as Caputo fractional derivative.

A Mittag-Leffler-type function of two variables

In this paper, we introduce and study a Mittag-Leffler-type function of two variables E1 (x, y) and a generalization of Mittag-Leffler-type function of one variable as limiting case of E1 (x, y), which includes several Mittag-Leffler-type functions of one variable as its special cases. Here, we first obtain the domain of convergence of E1 (x, y), considering all possible cases. Next, we give two differential equations for E1 (x, y) and one differential equation for for some particular values of the parameters. We further obtain two integral representations and Mellin–Barnes contour integral representation of E1 (x, y). We also obtain the Laplace transform of one and two dimensions of E1 (x, y) and its fractional integral and derivative. Next, we define an integral operator with E1 (x, y) as a kernel and show that it is bounded on the Lebesgue measurable space L(a, b). Finally, we introduce one more Mittag-Leffler-type function of two variables.