In this paper, we investigate the well-posedness for Cauchy problem multi-term time-fractional heat equation associated with Dunkl operator. The under consideration includes a linear combination of Caputo derivatives in time decreasing orders (0, 1) and positive constant coefficients one-dimensional operator.  To show solvability problem  use several important properties multinomial M...

In this study, the crystallization behavior of a 65GeO2-15PbO-10MgF2-10MgO glass (prepared by the conventional melt quenching technique) has been investigated. The microstructure and crystallization behaviors of this glass were characterized using X-ray diffraction (XRD), scanning electron microscopy (SEM), non-isothermal differential thermal analysis (DTA) and Fourier transform infrared spectr...

Some new properties of kernels of modified Kontorovitch–Lebedev integral transforms — modified Bessel functions of the second kind with complex orderK 1 2+iβ (x) are presented. Inequalities giving estimations for these functions with argument x and parameter β are obtained. The polynomial approximations of these functions as a solutions of linear differential equations with polynomial coefficie...

*Correspondence: Rudolf A. Treumann, International Space Science Institute, ISSI, Hallerstrasse 6, CH-3012 Bern, Switzerland e-mail: [email protected] A new form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral equat...

We consider a singular second order differential operator ∆ defined on ]0,∞[. We give nice estimates for the kernel which intervenes in the integral transform of the eigenfunction of ∆. Using these results, we establish Hardy type inequalities for Riemann-Liouville and Weyl transforms associated with the operator ∆.

An infinite dam with compound Poisson inputs and a statedependent release rate is considered. For this dam, we solve Kolmogorov’s backward differential equation to obtain the Laplace transforms of the first exit times in terms of a certain positive kernel. This allows us to provide an explicit expression for the Laplace transform of the wet period for a finite dam.

The time-dependent Schrödinger equation for two quite general types of perturbation has been solved by introducing the Laplace transforms to eliminate the time variable. The resulting time-independent differential equation can then be solved by the perturbation method, the variation method, the variation-perturbation method, and other methods.

We explore the possibility of using the method of classical integral transforms to solve a class of q-difference-differential equations. The Laplace and the Mellin transform of q-derivatives are derived. The results show that the Mellin transform of the qderivative resembles most closely the corresponding expression in classical analysis, and it could therefore be useful in solving certain q-di...

A linear (partial) functional system consists of linear partial differential, difference equations or any mixture thereof. We present an algorithm that determines whether linear functional systems are ∂-finite, and transforms ∂-finite systems to fully integrable ones. The algorithm avoids using Gröbner bases in Laurent–Ore modules when ∂-finite systems correspond to finitedimensional Ore module...

In this paper we have studied the unsteady flow of an electrically conducting viscous, incompressible dusty fluid flowing between two oscillating plates. The fluid is acted upon by a constant magnetic field perpendicular to the plates. Exact velocities of fluid and dust particles are derived by using differential geometry techniques and Laplace transforms. AMS Mathematics Subject Classification...