Comments on “Application of generalized differential transform method to multi-order fractional differential equations”, Vedat Suat Erturk,Shaher Momani,Zaid Odibat [Commun Nonlinear Sci Numer Simul 2008;13:1642–54]

In this note, we would like to point some similarities between the study [Erturk VS, Momani S, Odibat Z. Application of generalized differential transform method to multi-order fractional differential equations. Commun Nonlinear Sci Numer Simul. doi:10.1016/j.cnsns.2007.02.006] with the already existing one [Arikoglu A, Ozkol I. Solution of fractional differential equations by using differential transform method. Chaos Soliton Fract. 10.1016/j.chaos.2006.09.004].     

Corrigendum to “Third-order partial differential equations arising in the impulsive motion of a flat plate” [Commun Nonlinear Sci Numer Simulat 2009;14:2629–36]

We correct an oversight in our recently published paper Van Gorder and Vajravelu [Third-order partial differential equations arising in the impulsive motion of a flat plate. Commun Nonlinear Sci Numer Simulat 2009;14:2629–36], regarding the correct form of the boundary condition in Stokes’ first problem for the impulsive motion of an infinite flat plate. We present the corrected solution to the flow problem.     

Comments on: “Synchronization of N-coupled fractional-order chaotic systems with ring connection” [Commun Nonlinear Sci Numer Simulat 2010;15:401–12]

In this note, we present some points to paper [Tang Yang, Fang Jian-an, Synchronization of N-coupled fractional-order chaotic systems with ring connection. Commun Nonlinear Sci Numer Simulat 2010;15:401–12].     

Comment on: “Some exact solutions of KdV equation with variable coefficients” [Commun Nonlinear Sci Numer Simul 2011;16:1783–86]

It is shown that in the commented paper the exact solutions were found only for those variable-coefficient KdV equations which are reduced to the classical (constant-coefficient) KdV equation by point transformations, and these solutions are preimages of well-known traveling wave solutions of the KdV equation with respect to the corresponding point transformations. The equivalence-based approach suggested in [Popovych RO, Vaneeva OO. More common errors in finding exact solutions of nonlinear differential equations: Part I. Commun Nonlinear Sci Numer Simul 2010;15:3887–99] allows one to obtain more results. This disproves the relevance of the extended mapping transformation method for the class of equations under consideration.     

Comments on “Similarity variables and reduction of the heat equation on torus” [Commun Nonlinear Sci Numer Simulat 2012;17:1251–57]

A brief account of symmetry analysis of heat equation on torus is presented, correcting errors in a recently published paper.     

Reply to “Comments on “Fuzzy fractional order sliding mode controller for nonlinear systems,Commun Nonlinear Sci Numer Simulat 15 (2010) 963–978” ”

The aim of this letter is to confirm the achievements in [1] and answer all the mentioned comments in [2]. Meanwhile some other drawbacks in the comment paper [2] are also presented in this paper.     

Remarks on the “Reply to Comments on “Fuzzy fractional order sliding mode controller for nonlinear systems,Commun Nonlinear Sci Numer Simulat 15 (2010) 963–978””

In this letter, we show that the main results of the reply paper [1] are wrong. We demonstrate that the authors of Delavari et al. (2012) [1] have carried out an essential flaw in the proof approach of the system stability. Therefore, we prove that the defects of the paper [2] which have been described in the comment paper [3] are still continued. In this regard, we conclude that the results of our comment paper [3] are correct.     

Comment on “Parameter identification and synchronization of fractional-order chaotic systems” [Commun Nonlinear Sci Numer Simulat 2012;17:305–16]

This paper comments on the recently published work related to parameter identification of fractional-order chaotic systems [1]. In this note, it is shown that according to the sensitivity issues of chaotic systems to their initial conditions, the criteria for the cost function to be acceptable are not satisfied.     

Comment on: The (G′/G)-expansion method for the nonlinear lattice equations [Commun Nonlinear Sci Numer Simulat 17 (2012) 3490–3498]

We show that two of the nonlinear lattice equations studied by Ayhan & Bekir [Commun Nonlinear Sci Numer Simulat 17 (2012) 3490–3498] have already been investigated by Aslan [Commun Nonlinear Sci Numer Simulat 15 (2010) 1967–1973] using an improved version of the same method. The solutions obtained by the latter one include the solutions obtained by the former one.     

Comment on “Effects of the slip boundary condition on non-Newtonian flows in a channel” [Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 1377–1384]

Recently, Ellahi [1] discussed the slip effects on the flows of an Oldroyd 8-constant fluid using the homotopy analysis method. Crucial flaws in [1] are pointed out in this comment. The present paper provides an exact solution and a numerical solution by shooting method using Runge–Kutta algorithm of the flow problems considered in [1] with the correct nonlinear boundary conditions.     

Comments on “Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control” [Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762]

In this note some points to paper [L. Pan, W. Zhou, J. Fang, D. Li, Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control, Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762] are presented. Hereby, we illustrate that the way that authors in [1] treat with fractional version of Lyapunov stability theorem suffers lack of a correct justification.