Laplace Transform Method for Economic Models with Constant Proportional Caputo Derivative

The Laplace transform method for Burgers’ equation

The Laplace transform method (LTM) is introduced to solve Burgers’ equation. Because of the nonlinear term in Burgers’ equation, one cannot directly apply the LTM. Increment linearization technique is introduced to deal with the situation. This is a key idea in this paper. The increment linearization technique is the following: In time level t , we divide the solution u(x, t) into two parts: u(...

Inverse Laplace transform method for multiple solutions of the fractional Sturm-Liouville problems

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.

Nonlinearities distribution Laplace transform-homotopy perturbation method

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we ...

Fuzzy laplace transform on two order derivative and solving fuzzy two order differential equations

Classroom note: Fourier method for Laplace transform inversion

A method is described for inverting the Laplace transform. The performance of the Fourier method is illustrated by the inversion of the test functions available in the literature. Results are shown in the tables.