The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It shown that the derivative integral operators are bounded. Some fundamental characteristics of new operators, such as semi-group inverse characteristics, studied. As special cases these novel several already well known in literature acquired. generalized Laplace transform evaluated. By ...

The traditional theory of Laplace transformation (TLT) as it was put forward by Gustav Doetsch was principally intended to provide an operator calculus for ordinary derivable functions of the t-domain. As TLT does not account for the behavior of the inverse L-transform at t = 0 its validity is essentially confined to t > 0. However, from solutions of linear differential equations (DEs) one can ...

By using the numerical inverse Laplace transform based on modified Prudnikov formula, we construct solution of a nonstationary problem heat conduction for thermally sensitive half space operating in contact with layer under conditions convective exchange medium constant temperature. The thermoelastic state this piecewise homogeneous structure is investigated case where temperature kept surface.

The traditional theory of Laplace transformation (TLT) as it was put forward by Gustav Doetsch was principally intended to provide an operator calculus for ordinary derivable functions of the t-domain. As TLT does not account for the behavior of the inverse L-transform at t = 0 its validity is essentially confined to t > 0. However, from solutions of linear differential equations (DEs) one can ...

The spherical phylon group and invariants of the Laplace transform. Abstract We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of R d that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform.

The present work is aimed at analyzing the thermoelastic disturbances in a circular plate of finite thickness and infinite extent subjected to constant initial temperature and axisymmetric heat supply. Integral transform technique is used. Analytic solutions for temperature, displacement and stresses are derived within the context of unified system of equations in generalized thermoelasticity i...

This paper considers two flexible classes of omnibus goodness-of-fit tests for the inverse Gaussian distribution. The test statistics are weighted integrals over the squared modulus of some measure of deviation of the empirical distribution of given data from the family of inverse Gaussian laws, expressed by means of the empirical Laplace transform. Both classes of statistics are connected to t...

A time scale is any closed subset of the real line. Continuous time and discrete time are special cases. The unilateral Laplace transform of a signal on a time scale subsumes the continuous-time unilateral Laplace transform, and the discretetime unilateral z-transform as special cases. The regions of convergence (ROCs) time scale Laplace transforms are determined by the time scale’s graininess....