A review on harmonic wavelets and their fractional extension

C Cattani - Journal of Advanced Engineering and Computation, 2018 - jaec.vn
In this paper a review on harmonic wavelets and their fractional generalization, within the
local fractional calculus, will be discussed. The main properties of harmonic wavelets and …

Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method

F Mirzaee, E Solhi, S Naserifar - Applied Mathematics and Computation, 2021 - Elsevier
In this paper, an attractive idea using moving least squares (MLS) and spectral collocation
method is extended to estimate the solution of nonlinear stochastic Volterra integro …

Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion

MH Heydari, MR Mahmoudi, A Shakiba… - … in Nonlinear Science …, 2018 - Elsevier
In this paper, a new computational method is proposed to solve a class of nonlinear
stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm). The …

[图书][B] Wavelet analysis: basic concepts and applications

S Arfaoui, AB Mabrouk, C Cattani - 2021 - taylorfrancis.com
Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained
introduction to the ideas underpinning wavelet theory and its diverse applications. This book …

Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion

MH Heydari, Z Avazzadeh, MR Mahmoudi - Chaos, Solitons & Fractals, 2019 - Elsevier
This paper is concerned with a computational approach based on the Chebyshev cardinal
wavelets for a novel class of nonlinear stochastic differential equations characterized by the …

[PDF][PDF] New and effective solitary applications in Schrödinger equation via Brownian motion process with physical coefficients of fiber optics

YF Alharbi, EK El-Shewy, MAE Abdelrahman - AIMS Math, 2023 - aimspress.com
Using the unified solver technique, the rigorous and effective new novel optical progressive
and stationary structures are established in the aspects of hyperbolic, trigonometric, rational …

Chebyshev polynomials for generalized Couette flow of fractional Jeffrey nanofluid subjected to several thermochemical effects

R Roohi, MH Heydari, O Bavi, H Emdad - Engineering with Computers, 2021 - Springer
The generalized Couette flow of Jeffrey nanofluid through porous medium, subjected to the
oscillating pressure gradient and mixed convection, is numerically simulated using variable …

Moving least squares and spectral collocation method to approximate the solution of stochastic Volterra–Fredholm integral equations

F Mirzaee, E Solhi, N Samadyar - Applied Numerical Mathematics, 2021 - Elsevier
In this article, an idea based on moving least squares (MLS) and spectral collocation method
is used to estimate the solution of nonlinear stochastic Volterra–Fredholm integral equations …

Orthonormal Bernoulli polynomials collocation approach for solving stochastic Itô‐Volterra integral equations of Abel type

N Samadyar, F Mirzaee - International Journal of Numerical …, 2020 - Wiley Online Library
In this paper, orthonormal Bernoulli collocation method has been developed to obtain the
approximate solution of linear singular stochastic Itô‐Volterra integral equations. By …

Accurate and stable numerical method based on the Floater-Hormann interpolation for stochastic Itô-Volterra integral equations

F Mirzaee, S Naserifar, E Solhi - Numerical Algorithms, 2023 - Springer
In various fields of science and engineering, such as financial mathematics, mathematical
physics models, and radiation transfer, stochastic integral equations are important and …