Approximate analytical solution of the nonlinear fractional KdV–Burgers equation: a new iterative algorithm

A El-Ajou, OA Arqub, S Momani - Journal of Computational Physics, 2015 - Elsevier
In this paper, explicit and approximate solutions of the nonlinear fractional KdV–Burgers
equation with time–space-fractional derivatives are presented and discussed. The solutions …

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation

XJ Yang, JA Tenreiro Machado, D Baleanu… - … Journal of Nonlinear …, 2016 - pubs.aip.org
This paper investigates the Korteweg-de Vries equation within the scope of the local
fractional derivative formulation. The exact traveling wave solutions of non-differentiable …

A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approach

XJ Yang, JAT Machado, HM Srivastava - Applied Mathematics and …, 2016 - Elsevier
In this article, we first propose a new numerical technique based upon a certain two-
dimensional extended differential transform via local fractional derivatives and derive its …

Solving time-fractional Navier–Stokes equations using homotopy perturbation Elzaki transform

RM Jena, S Chakraverty - SN Applied Sciences, 2019 - Springer
In this article, a hybrid technique called homotopy perturbation Elzaki transform method has
been applied to solve Navier–Stokes equation of fractional order. In the hybrid technique …

Numerical solutions of the space-and time-fractional coupled Burgers equations by generalized differential transform method

J Liu, G Hou - Applied Mathematics and Computation, 2011 - Elsevier
In this paper, by introducing the fractional derivative in the sense of Caputo, the generalized
two-dimensional differential transform method (DTM) is directly applied to solve the coupled …

On convergence of homotopy analysis method and its application to fractional integro-differential equations

S Abbasbandy, MS Hashemi… - Quaestiones Mathematicae, 2013 - Taylor & Francis
In this paper, we have used the homotopy analysis method (HAM) to obtain approximate
solution of fractional integro-differential equations (FIDEs). Convergence of HAM is …

An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method

Hajira, H Khan, A Khan, P Kumam, D Baleanu… - Advances in Difference …, 2020 - Springer
In this article, a hybrid technique of Elzaki transformation and decomposition method is used
to solve the Navier–Stokes equations with a Caputo fractional derivative. The numerical …

[PDF][PDF] The first integral method for exact solutions of nonlinear fractional differential equations

A Bekir, Ö Güner, Ö Ünsal - Journal of Computational and …, 2015 - researchgate.net
In this paper, we establish exact solutions for some nonlinear fractional differential equations
(FDEs). The first integral method with help of the fractional complex transform (FCT) is used …

Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique

A Akgül, M Inc, E Karatas, D Baleanu - Advances in Difference Equations, 2015 - Springer
In this work, we study the fractional order Lane-Emden differential equations by using the
reproducing kernel method. The exact solution is shown in the form of a series in the …

Status of the differential transformation method

C Bervillier - Applied Mathematics and Computation, 2012 - Elsevier
Further to a recent controversy on whether the differential transformation method (DTM) for
solving a differential equation is purely and solely the traditional Taylor series method, it is …