In this note, we review some important results on wavelets, together with their main applications. Similarly, present the fractional calculus and current applications in pure applied science. We conclude paper showing close interconnection between wavelet analysis calculus.

Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems FDEs. The main goal method is convert FDE into a system algebraic equations that can be easily solved using matrix methods. In order achieve this, we first generate operational matrices for fractional integration and block-pulse functions (BPF) function approximation. Since obtained sparse, numerical fast...

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory—including some new extensions for fractional orders—in a se...

This paper is devoted to study a computation scheme to approximate solution of fractional differential equations(FDEs) and coupled system of FDEs with variable coefficients. We study some interesting properties of shifted Legendre polynomials and develop a new operational matrix. The new matrix is used along with some previously derived results to provide a theoretical treatment to approximate ...

In this paper, an efficient and accurate computational method based on the Chebyshev wavelets (CWs) together with spectral Galerkin method is proposed for solving a class of nonlinear multi-order fractional differential equations (NMFDEs). To do this, a new operational matrix of fractional order integration in the Riemann-Liouville sense for the CWs is derived. Hat functions (HFs) and the collo...

Abstract This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As matter of fact, the (VFD) that has been used is in Caputo sense. The first step this constructive on construction using shifted Legendre–Laguerre polynomials unknown coefficients. second involves combination collocation method and operatio...

In this paper, we mainly concentrate on the recognition module of an object detection and recognition system. Two types of images, visible and infrared, are investigated in order to improve the objects detection and recognition process. Different types of mother wavelets (Haar, Daubechies, Coiflet, Symlet, Biorthogonal, Fractional causal or generalized, etc.) are used to extract the wavelet coe...