On the fractional signals and systems

R Magin, MD Ortigueira, I Podlubny, J Trujillo - Signal Processing, 2011 - Elsevier
A look into fractional calculus and their applications from the signal processing point of view
is done in this paper. A coherent approach to the fractional derivative is presented, leading …

An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering

JH He - International Journal of Modern Physics B, 2008 - World Scientific
This review is an elementary introduction to the concepts of the recently developed
asymptotic methods and new developments. Particular attention is paid throughout the …

[图书][B] Fractional derivative modeling in mechanics and engineering

W Chen, HG Sun, X Li - 2022 - Springer
Classic Newtonian mechanics assumes that space and time are continuous everywhere.
The basic physical quantities (eg speed, acceleration and force) can be described by an …

[图书][B] Fractional derivatives for physicists and engineers

VV Uchaikin - 2013 - Springer
“God made the integers; all else is the work of man” 1. For centuries, the ancients were
satisfied with using natural numbers called simply “numbers”. What we call irrational …

[HTML][HTML] Variational iteration method: new development and applications

JH He, XH Wu - Computers & Mathematics with Applications, 2007 - Elsevier
Variational iteration method has been favourably applied to various kinds of nonlinear
problems. The main property of the method is in its flexibility and ability to solve nonlinear …

Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

Y Li, W Zhao - Applied mathematics and computation, 2010 - Elsevier
Haar wavelet operational matrix has been widely applied in system analysis, system
identification, optimal control and numerical solution of integral and differential equations. In …

[HTML][HTML] The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics

Z Odibat, S Momani - Computers & Mathematics with Applications, 2009 - Elsevier
Variational iteration method has been used to handle linear and nonlinear differential
equations. The main property of the method lies in its flexibility and ability to solve nonlinear …

Solving differential equations of fractional order using an optimization technique based on training artificial neural network

M Pakdaman, A Ahmadian, S Effati… - Applied Mathematics …, 2017 - Elsevier
The current study aims to approximate the solution of fractional differential equations (FDEs)
by using the fundamental properties of artificial neural networks (ANNs) for function …

The homotopy perturbation method for fractional differential equations: part 1 Mohand transform

M Nadeem, JH He, A Islam - … Journal of Numerical Methods for Heat & …, 2021 - emerald.com
Purpose This study aims that very lately, Mohand transform is introduced to solve the
ordinary and partial differential equations (PDEs). In this paper, the authors modify this …

[HTML][HTML] A study on the convergence of variational iteration method

ZM Odibat - Mathematical and Computer Modelling, 2010 - Elsevier
Variational iteration method has been widely used to handle linear and nonlinear models.
The main property of the method is its flexibility and ability to solve nonlinear equations …