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Approximate analytical solution of the nonlinear fractional KdV–Burgers equation: a new iterative algorithm
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 …
equation with time–space-fractional derivatives are presented and discussed. The solutions …
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
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 …
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
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 …
dimensional extended differential transform via local fractional derivatives and derive its …
Solving time-fractional Navier–Stokes equations using homotopy perturbation Elzaki transform
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 …
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 …
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
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 …
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
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 …
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
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 …
(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
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 …
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 …
solving a differential equation is purely and solely the traditional Taylor series method, it is …