In the present study, the boundary value problems in generalized thermodiffusive elastic medium has been investigated as a result of inclined load. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. As an application of t...

In this paper, we establish two approximation theorems for the multidimensional fractional Fourier transform via appropriate convolutions. As applications, study boundary and initial problems of Laplace heat equations with chirp functions. Furthermore, obtain general Heisenberg inequality respect to transform.

In addition to their inestimable importance in mathematics and its applications, Fourier series also serve as the entry point into the wonderful world of Fourier analysis and its wide-ranging extensions and generalizations. An entire industry is devoted to further developing the theory and enlarging the scope of applications of Fourier–inspired methods. New directions in Fourier analysis contin...

Abstract: Integral expressions for positive-part moments E Xp + (p > 0) of random variables X are presented, in terms of the Fourier-Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-par...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski’s coagulation equations for the solvable kernels K(x, y) = 2, x+ y and xy. We prove the uniform convergence of densities to the self-similar solution with exponential tails under the regularity hypothesis that a suitable moment have an integrable Fourier transform. For the discrete equations we prove uniform conv...

— We show that the limit, by rescaling, of the ‘new supersymmetric index’ attached to the Fourier-Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of comple...

Introduction: Transformations are vital to any engineering subject, in particular, to electrical engineering. Fourier series, Laplace transform, Fourier transform and their counterparts in the discrete-time domain, are the fundamental tools for signal processing, communication and control engineering. Recently, the discrete Pascal transform (DPT) has been introduced to process discrete signals ...