In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...

Time scale dependence on the working nature of wavelet analysis makes it a valuable tool for Hurst parameter estimation. Similar to other wavelet-based signal processing applications, the selection of a particular wavelet type and vanishing moment in wavelet based Hurst estimation is a challenging problem. In this paper, we investigate the best Daubechies wavelet in wavelet based Hurst estimati...

A linearized spectral Galerkin/finite difference approach is developed for variable fractional-order nonlinear diffusion–reaction equations with a fixed time delay. The temporal discretization the variable-order fractional derivative performed by L1-approximation. An appropriate basis function in terms of Legendre polynomials used to construct Galerkin method spatial second-order operator. main...

In this paper we study some problems related with the theory of multidimensional p-adic wavelets in connection with the theory of multidimensional p-adic pseudo-differential operators (in the p-adic Lizorkin space). We introduce a new class of n-dimensional p-adic compactly supported wavelets. In one-dimensional case this class includes the Kozyrev p-adic wavelets. These wavelets (and their Fou...

Our aim is to propose a multi-dimensional operator framework that provides a bridge between approximation theory (in particular, the construction of polyharmonic splines and wavelets) and the investigation of self-similar stochastic processes. Our investigation starts with the identification of the linear differential operators that are translation-, scaleand rotation-invariant; these are the f...

The mathematical model of steady state mono-layer potentiometric biosensor is studied and the model is based on nonstationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents a numerical method based on Legendre wavelets operational matrix method. These results are compared with available limiting case results a...