In this paper, the local fractional Laplace decomposition method is implemented to obtain approximate analytical solution of the telegraph and Laplace equations on Cantor sets. This method is a combination of the Yang-Laplace transform and the Adomian decomposition method. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to ...

The unsteady flow of a visco-elastic Maxwell fluid through a rectilinear pipe having its cross-section as a parallelogram under the influence of a axial pressure gradient (I) varying linearly with time , and (II) decreasing exponentially with time has been discussed in the present paper. Variables separable and Laplace transform methods have been used to solve the problem.  

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

Inverting the Laplace transform is a paradigm for exponentially ill-posed problems. For a class of operators, including the Laplace transform, we give forward and inverse formulae that have fast implementations using the fast Fourier transform. These formulae lead easily to regularized inverses whose effects on noise and filtered data can be precisely described. Our results give cogent reasons ...

Abstract—Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed ...

Abstract: This paper aims to apply the Laplace transform for solving linear fractional-order differential equation. The Laplace transform is a powerful tool in applied mathematics and engineering. It will allow us to transform fractional differential equations into algebraic equations and then by solving this algebraic equations, we can obtain the unknown function by using the Inverse Laplace T...

In this paper we will investigate the semi-markov random processes with positive tendency, negative jumps and delaying boundary at zero in this article. The Laplace transform on time, Laplace-Stieltjes transform on phase of the conditional and unconditional distributions and Laplace-Stieltjes transform of the ergodic distribution are defined. The characteristics of the ergodic distribution will...