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 …

[HTML][HTML] Cubic B-spline approximation for linear stochastic integro-differential equation of fractional order

F Mirzaee, S Alipour - Journal of Computational and Applied Mathematics, 2020 - Elsevier
In this paper, the cubic B-spline collocation method is used for solving the stochastic integro-
differential equation of fractional order. we show that stochastic integro-differential equation …

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 …

A new wavelet method for variable‐order fractional optimal control problems

MH Heydari, Z Avazzadeh - Asian Journal of Control, 2018 - Wiley Online Library
In this paper, a new computational method based on the Legendre wavelets (LWs) is
proposed for solving a class of variable‐order fractional optimal control problems (V …

[HTML][HTML] New exact solitary wave solutions, bifurcation analysis and first order conserved quantities of resonance nonlinear Schrödinger's equation with Kerr law …

A Jhangeer, HM Baskonus, G Yel, W Gao - Journal of King Saud University …, 2021 - Elsevier
This paper anatomizes the exact solutions of the resonant non-linear Schrödinger's equation
(R-NLSE) with the Kerr law non-linearity with the assistance of the new extended direct …

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 …

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 …

[HTML][HTML] Euler polynomial solutions of nonlinear stochastic Itô–Volterra integral equations

F Mirzaee, N Samadyar, SF Hoseini - Journal of Computational and …, 2018 - Elsevier
In this study, a practical matrix method based on operational matrices of integration and
collocation points is presented to find the approximate solution of nonlinear stochastic Itô …

[HTML][HTML] Fibonacci wavelet based numerical method for the solution of nonlinear Stratonovich Volterra integral equations

SC Shiralashetti, L Lamani - Scientific African, 2020 - Elsevier
This article provides an effective technique to solve nonlinear Stratonovich Volterra integral
equations (NSVIE). These equations can be reduced to a system of nonlinear algebraic …