In this paper, Adomian decomposition method (ADM) and Laplace decomposition method (LDM) used to obtain series solutions of Burgers-Huxley and Burgers-Fisher Equations. In ADM the algorithm is illustrated by studying an initial value problem and LDM is based on the application of Laplace transform to nonlinear partial differential equations. In ADM only few terms of the expansion are required t...

Abstract. In this paper we consider the Laplace transforms of some random series, in particular, the random series derived as the squared L2 norm of a Gaussian stochastic process. Except for some special cases, closed form expressions for Laplace transforms are, in general, rarely obtained. It is the purpose of this paper to show that for many Gaussian random processes the Laplace transform can...

Abstract The present work considers a two-dimensional (2D) heat conduction problem in the semi-infinite domain based on classical Fourier model and other non-Fourier models, e.g., Maxwell–Cattaneo–Vernotte (MCV) equation, parabolic, hyperbolic, modified hyperbolic dual-phase-lag (DPL) equations. Using integral transform technique, Laplace, transforms, we provide solution of (Green’s function) L...

In this paper, four types of fractional Fourier cosine and sine Laplace weighted convolutions are defined, the corresponding convolution theorems associated with transform, transform derived in detail. Furthermore, relationship between (sine) existing studied, Young's type theorem is also investigated. addition, as an application for (sine)-Laplace convolution, system convolution-type integral ...

1 Fourier Transform 1 1.1 Properties of the Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Schwartz space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Convergence in S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fourier Transform in L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Fouri...

Small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. Moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. Non-Fourier heat transfer overcomes some shortcomings of Fourier heat tran...

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...

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

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.