A direct method for solving variational problems using Legendre wavelets is presented. An operational matrix of integration is first introduced and is utilized to reduce a variational problem to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. © 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

Zero-watermarking methods provide promising solutions and impressive performance for copyright protection of images without changing the original images. In this paper, a novel zero-watermarking method color is envisioned. Our envisioned approach based on multi-channel orthogonal Legendre Fourier moments fractional orders, referred to as MFrLFMs. method, highly precise Gaussian integration util...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...

Wavelet transforms or wavelet analysis represent a recently created mathematical tool for assistance in resolving various issues. Wavelets can also be used numerical analysis. In this study, we solve pantograph delay differential equations using the Modified Laguerre method (MLWM), an effective technique. Fractional derivatives are defined Caputo operator. The convergence of suggested strategy ...

We extend Schoenberg’s family of polynomial splines with uniform knots to all fractional degrees α > −1. These splines, which involve linear combinations of the one-sided power functions x+ = max(0, x) α, are α-Hölder continuous for α > 0. We construct the corresponding B-splines by taking fractional finite differences and provide an explicit characterization in both time and frequency domains....

Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional wave equation (FWE) is considered. The fractional derivative is described in the Caputo sense. The method is...