Homotopy analysis method for the fractional nonlinear equations
Bahman Ghazanfari,F. Veisi +1 more
TLDR
In this article, the homotopy analysis method is extended to investigate the numerical solutions of the fractional nonlinear wave equation and the numerical results validate the convergence and accuracy of the method.About:
This article is published in Journal of King Saud University - Science.The article was published on 2011-10-01 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Homotopy analysis method & Adomian decomposition method.read more
Citations
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Journal ArticleDOI
Thermo-diffusion and diffusion-thermo effects on flow of second grade fluid between two inclined plane walls
TL;DR: In this paper, the problem of second grade fluid between two nonparallel walls having a source or a sink at the cusp is explored, where Soret and Dufour effects are incorporated in the energy and concentration equations.
Journal ArticleDOI
Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation
TL;DR: The review is devoted to using the fractional integro-differential calculus for description of the dynamics of various systems and control processes.
Dynamical Behaviors of Separated Homotopy Method Defined by Conformable Operator
TL;DR: In this paper, the authors considered linear/nonlinear differential equations (DEs) containing conformable derivative operator (CDO) and obtained approximate solutions of these mentioned DEs in the form of infinite series which converges swiftly to its exact value by using separated homotopy method (SHM).
Book ChapterDOI
Discussing a Solution to Nonlinear Duffing Oscillator with Fractional Derivatives Using Homotopy Analysis Method (HAM)
TL;DR: In this article, the authors obtained an analytic solution to the initial valued problem of the Duffing oscillator with fractional order derivative using the Homotopy analysis method (HAM) to obtain the said analytic solution.
Journal ArticleDOI
Dynamic behaviors of a fractional order nonlinear oscillator
TL;DR: In this paper, the primary resonance of a special type of nonlinear Duffing oscillator with fractional-order derivative is studied by the averaging method, and the effects of the some parameters such as fractional order, nonlinear coefficients and force amplitude on the system dynamics are investigated.
References
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Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Book
Beyond Perturbation: Introduction to the Homotopy Analysis Method
Shijun Liao,SA Sherif +1 more
TL;DR: In this paper, a simple bifurcation of a nonlinear problem multiple solutions of a Nonlinear Problem Nonlinear Eigenvalue Problem Thomas-Fermi Atom Model Volterra's Population Model Free Oscillation Systems with Odd Nonlinearity Free oscillations with Quadratic nonlinearity Limit Cycle in a Multidimensional System Blasius' viscous flow Boundary-layer Flow Boundarylayer Flow with Exponential Property Boundary Layer Flow with Algebraic Property Von Karman Swirling Flow Nonlinear Progressive Waves in Deep Water BIBLIOGR
Journal ArticleDOI
On the homotopy analysis method for nonlinear problems
TL;DR: A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e. the algebraically decaying viscous boundary layer flow due to a moving sheet.
Book
Physics of Fractal Operators
TL;DR: In this article, the authors describe the behavior of complex systems and show how the fractional calculus can be used to model the behavior, such as systems with long-range spatial interactions or long-time memory.
Related Papers (5)
Solution of nonlinear fractional differential equations using homotopy analysis method
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Mehdi Ganjiani,Hossein Ganjiani +1 more