Wavelet methods for solving fractional order differential equations
type: Item
instance of: scholarly article
title: Wavelet methods for solving fractional order differential equations
zbMATH Open document ID: 1407.65331
DOI: 10.1155/2014/140453
author: Erdal Karapınar
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linear and nonlinear fractional differential equations. Our goal is to analyze the selected wavelet methods and assess their accuracy and efficiency with regard to solving fractional differential equations. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on various wavelets in order to solve differential equations of arbitrary order.
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 7015770
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/140453
OpenAlex ID: W1985540374
Wikidata QID: Q59063129
cites work: Q4791729
cites work: Q4003151
cites work: Q4233638
cites work: Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method
cites work: Approximate analytical solution for seepage flow with fractional derivatives in porous media
cites work: On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation
cites work: A new approach for the application of Adomian decomposition method for the solution of fractional space diffusion equation with insulated ends
cites work: Analytical Solution of a Dynamic System Containing Fractional Derivative of Order One-Half by Adomian Decomposition Method
cites work: Exact solutions for time-fractional diffusion-wave equations by decomposition method
cites work: Haar wavelet operational methods for the numerical solutions of fractional order nonlinear oscillatory Van der Pol system
cites work: The Legendre wavelet method for solving fractional differential equations
cites work: Approximate solution of fractional nonlinear partial differential equations by the Legendre multiwavelet Galerkin method
cites work: Solving a nonlinear fractional differential equation using Chebyshev wavelets
cites work: Wavelet-Galerkin method for the solution of shear wave equation
cites work: Fast wavelet transforms and numerical algorithms I
cites work: Haar wavelet method for solving lumped and distributed-parameter systems
cites work: Adaptive Multiresolution Collocation Methods for Initial-Boundary Value Problems of Nonlinear PDE<scp>s</scp>
cites work: Cubic spline wavelet bases of Sobolev spaces and multilevel interpolation
cites work: Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet
cites work: Kronecker operational matrices for fractional calculus and some applications
cites work: The second kind Chebyshev wavelet method for solving fractional differential equations
cites work: The Legendre wavelets operational matrix of integration
description: scientific article; zbMATH DE number 7015770