and integral calculus from integer orders n to the entire complex plane. Methods are presented for using this generalized calculus with Laplace transforms of complex-order derivatives to solve analytically many differential equations in physics, facilitate numerical computations, and generate new infinite-series representations of functions. As examples, new exact analytic solutions of differen...

This paper touches upon several traditional topics of 1D linear complex analysis including distribution of zeros of entire functions, completeness problem for complex exponentials and for other families of special functions, some problems of spectral theory of selfadjoint differential operators. Their common feature is the close relation to the theory of complex Fourier transform of compactly s...

We consider a numerical solution of the stochastic moving boundary value problem, whose existence and uniqueness of solution are proved in [16]. Numerical approximations are based on the transformation which transforms the stochastic moving boundary problem whose spatial domain is a priori unknown to a nonlinear stochastic partial differential equation which has a fixed spatial domain. We const...

The present paper investigates the reliability and sensitivity analysis of a coal handling unit of a thermal power plant using a probabilistic approach. Coal handling unit is the main block of a thermal power plant and it is necessary for a good function of a power plant that its power supply, which is dealt in coal handling unit, must function continuously without any obstacle. The configurati...

Cu2O nanoparticles were synthesized by thermal treatment in liquid paraffin without any inert gas protection using nano structures of Schiff base copper (II) complex (1) as precursor. Liquid paraffin was used as solvent and reductant. Span 80 was applied to control the morphology of cuprous oxide nanoparticles. The nano structure of the complex was characterized by X-ray diffraction measurement...

This communication influences on magnetohydrodynamic flow of viscoelastic fluid with magnetic field induced by oscillating plate. General solutions have been found out for velocity and shear stress profiles using mathematical transformations (Integral transforms). The governing partial differential equations have been solved analytically under boundary conditions u(0,t)=A_0 H(t)sinΩt and u(0,t)...

In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...

A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area...

This paper deals with linear stochastic partial differential equations variable coefficients driven by Lévy white noise. First, an existence theorem for integral transforms of noise is derived and the generalized mild solutions second order elliptic proved. Further, electric Schrödinger operator different potential functions V discussed.