Discrete spectrum Analysis using Laplace transform and Volterra equations (DALV-method)

Yang-Laplace transform method Volterra and Abel's integro-differential equations of fractional order

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...

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations

The analytical solutions for Volterra integro-differential equations within Local fractional operators by Yang-Laplace transform

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 ...

Spectrum Analysis Using the Discrete Fourier Transform ∗

The discrete Fourier transform (DFT) maps a nite number of discrete time-domain samples to the same number of discrete Fourier-domain samples. Being practical to compute, it is the primary transform applied to real-world sampled data in digital signal processing. The DFT has special relationships with the discrete-time Fourier transform and the continuous-time Fourier transform that let it be u...

A Laplace ladder of discrete Laplace equations

The notion of a Laplace ladder for a discrete analogue of the Laplace equation is presented. The adjoint of the discrete Moutard equation and a discrete counterpart of the nonlinear form of Goursat equation are introduced. 1 Notation Value of functions of continuous variables we denote by f(u, v) i.e. f : R ∋ (u, v) 7→ f(u, v) ∈ R while functions of discrete variables by f(m1, m2) i.e. f : Z 2 ...