Author
Reza Abazari
Other affiliations: Islamic Azad University, University of Tabriz
Bio: Reza Abazari is an academic researcher from University of Mohaghegh Ardabili. The author has contributed to research in topics: Nonlinear system & Hyperbolic function. The author has an hindex of 17, co-authored 47 publications receiving 811 citations. Previous affiliations of Reza Abazari include Islamic Azad University & University of Tabriz.
Papers
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TL;DR: The Differential Transformation Method (DTM) is employed to obtain the numerical/analytical solutions of the Burgers and coupled Burgers equations and is compared against three famous methods, namely the homotopy perturbation method, the Homotopy analysis method and the variational iteration method.
Abstract: In this paper, the Differential Transformation Method (DTM) is employed to obtain the numerical/analytical solutions of the Burgers and coupled Burgers equations. We begin by showing how the differential transformation method applies to the linear and nonlinear parts of any PDE and give some examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations. We also compare it against three famous methods, namely the homotopy perturbation method, the homotopy analysis method and the variational iteration method. These results show that the technique introduced here is accurate and easy to apply.
108 citations
TL;DR: In this article, a coupled version of a previous work on nonlinear Schrodinger equation was presented, where the authors applied the differential transformation method (DTM) to solving coupled Schroderg equations.
85 citations
TL;DR: In this paper, a generalized Hirota-Satsuma coupled KdV equation is solved using two semi-analytic methods, differential transform method (DTM) and reduced form of differential transformation method (so called RDTM).
74 citations
TL;DR: This work successfully extended two-dimensional differential transform method and their reduced form, by presenting and proving some theorems, to obtain the solution of partial differential equations (PDEs) with proportional delay in t and shrinking in x.
Abstract: In this work, we successfully extended two-dimensional differential transform method and their reduced form, by presenting and proving some theorems, to obtain the solution of partial differential equations (PDEs) with proportional delay in t and shrinking in x. Theorems are presented in the most general form to cover a wide range of PDEs, being linear or nonlinear and constant or variable coefficient. In order to show the power and robustness of the present methods and to illustrate the pertinent features of related theorems, some examples are presented.
63 citations
TL;DR: In this article, the G ′ G -expansion method is proposed for constructing more general exact solutions of the three nonlinear evolution equations arising in fluids science with physical interest, namely, Vakhnenko-Parkes equation, generalized regularized long wave (RLW) equation and symmetric regularized LW equation.
58 citations
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TL;DR: In this paper, the effect of the squeeze number, nanofluid volume fraction, Hartmann number and heat source parameter on flow and heat transfer was investigated, and the results showed that skin friction coefficient increases with increase of the Nusselt number and Hartmann numbers but it decreases with an increase in the volume fraction.
311 citations
TL;DR: In this paper, the (G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative.
Abstract: In this paper, the (G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann—Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota—Satsuma coupled KdV equations and the time-fractional fifth-order Sawada—Kotera equation. As a result, some new exact solutions for them are successfully established.
237 citations
TL;DR: In this paper, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie's modified Riemann-Liouville derivative.
227 citations
TL;DR: In this paper, three highly accurate and simple analytical methods, differential transformation method (DTM), Collocation Method (CM) and Least Square Method (LS), are applied for predicting the temperature distribution in a porous fin with temperature dependent internal heat generation.
174 citations
TL;DR: The asymptotic synchronization of coupled reaction–diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin.
Abstract: The asymptotic synchronization of coupled reaction–diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin. The main objectives of this brief are to save communication resources and to reduce the conservativeness of the obtained synchronization criteria, which are carried out from the following two aspects: 1) mode-dependent quantized control technique is designed to reduce control cost and save communication channels and 2) Wirtinger inequality is utilized to deal with the reaction–diffusion terms in a matrix form and reciprocally convex technique combined with new Lyapunov–Krasovskii functional is used to derive delay-dependent synchronization criteria. The obtained results are general and formulated by linear matrix inequalities. Moreover, combined with an optimal algorithm, control gains with the least magnitude are designed.
168 citations