The primary purpose of this research is to demonstrate an efficient replacement double transform called the Laplace–Sumudu (DLST) and prove some related theorems new transform. Also, we will discuss fundamental properties basic functions. Then, by utilizing those outcomes, apply it partial differential equations show its simplicity, efficiency, high accuracy.

Two new transforms with piecewise linear kernels are introduced. These analogues of the classical Laplace transform and Z-transform. Properties these investigated applications to ordinary differential equations integral provided. This article is ideal for study as a foundational project in an undergraduate course and/or equations.

A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the...

Abstract. A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function...

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governi...

A general analytical scheme for computing the n-fold convolution of exponentialsum distribution functions has been developed in this paper. The n-fold convolution is first expressed by multiple sums of recursive integrals. These recursive integrals are then reconstructed with a series of delta functions to avoid separations of integrations. Part of the recursive integrals has been solved analyt...

We develop a new efficient and analytically tractable method for estimation of parametric volatility models that is robust to price-level jumps and generally has good finite sample properties. The method entails first integrating intra-day data into the Realized Laplace Transform of volatility, which is a model-free and jump-robust estimate of daily integrated empirical Laplace transform of the...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

The main goal of this research is to present a new approach double transforms called the Laplace–ARA transform (DL-ARAT). This novel combination Laplace and ARA transforms. We basic properties including existence, linearity some results related partial derivatives convolution theorem. To obtain exact solutions, applied several differential equations such as Klein–Gordon equation, heat wave equa...