Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM

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.

https://iopscience.iop.org/article/10.1088/0253-6102/58/5/02/pdf

(G'/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics

The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics ✩

Heat transfer study through porous fins (Si3N4 and AL) with temperature-dependent heat generation

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.

Synchronization of Coupled Markovian Reaction–Diffusion Neural Networks With Proportional Delays Via Quantized Control

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.

Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation method

Numerical study of nonlinear Schrödinger and coupled Schrödinger equations by differential transformation method

Numerical simulation of generalized Hirota-Satsuma coupled KdV equation by RDTM and comparison with DTM

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.

Reza Abazari

Papers

Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation method

Numerical study of nonlinear Schrödinger and coupled Schrödinger equations by differential transformation method

Numerical simulation of generalized Hirota-Satsuma coupled KdV equation by RDTM and comparison with DTM

Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay

Application of G′G-expansion method to travelling wave solutions of three nonlinear evolution equation