<p style='text-indent:20px;'>In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace Whittaker K-transform Fourier transforms. Also found applications problem on fractional kinetic equation pertaining to function using Sumudu transform technique. Mittage-Leffler is use...

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classica...

The titled problem of coupled thermoelasticity for porous structure has been solved with an instantaneous heat source acting on a plane area in an unbounded medium. The basic equations of thermoelasticity, after being converted into a one-dimensional form, have been written in the form of a vector-matrix differential equation and solved by the eigenvalue approach for the field variables in the ...

We consider the subspace of Schwartz space rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in a multidimensional real equipped with topology defined by countable family norms constructed help separately radial ℝn. describe strong dual this terms Fourier–Laplace transform functionals.

Abstract Inspired by Jaming’s characterization of the Fourier transform on specific groups via convolution property, we provide a novel approach which characterizes any locally compact abelian group. In particular, our encompasses results. Furthermore, demonstrate that cosine as well Laplace can also be characterized suitable property.

In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes of the Heston (1993) type. We derive the associated partial differential equation (PDE) of the option price using hedging arguments and Ito’s lemma. An integral expression for the general solution of the PDE is presented b...

In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivatives. We provide closed form formulae for the Fourier transforms of vanilla a...

A general method for studying boundary value problems for linear and for integrable nonlinear partial differential equations in two dimensions was introduced in [3]. For linear equations in a convex polygon [2,4,5], this method: (a) Expresses the solution q(x,y) in the form of an integral (generalized inverse Fourier transform) in the complex k-plane involving a certain function q̂(k) (generaliz...