Paper's Title:

New Jacobi Elliptic Function Wave Solutions for Conformable Fractional Benjamin-Bona-Mahoney-Burgers Equation

Author(s):

Guechi Meriem, Guechi Fairouz

Department of Mathematics,
Faculty of Sciences,
LMFN, University Sétif1,
Algeria.
E-mail: guechi.meriem87@gmail.com
fairouz.chegaar@univ-setif.dz

Abstract:

In this paper, Jacobi elliptic function expansion method is applied to solve fractional Benjamin-Bona-Mahoney-Burgers equation with conformable derivative and power law nonlinearity. This method is straightforward, concise, effective and can be used for many other nonlinear evolution equations. Numerical solutions are given to illustrate the accuracy and validity of this method.

Paper's Title:

Numerical Study of a Mathematical Model of a Free-Surface Potential Flow

Author(s):

H. Serguine, F. Guechi and A. Gasmi

Department Of Mathematics, Faculty of Science,
Ferhat Abbas Universty, 19000, Setif,
Algeria.
E-mail: houria.serguine@univ-msila.dz

 
Department Of Mathematics, Faculty of Science,
Ferhat Abbas Universty, 19000, Setif,
Algeria.
E-mail:  fairouz.chegaar@univ-setif.dz

Laboratory of Pure and Applied Mathematics, Faculty of Mathematics and Computer Science,
Mohamed Boudiaf Universty, 28000, M'sila,
Algeria.
E-mail: abdelkader.gasmi@univ-msila.dz

Abstract:

In this work, the problem of a potential and two-dimensional flow with a free surface of an incompressible, irrotational and inviscid fluid of a jet in front an inclined wall is considered, where γ is the inclination angle with the horizontal. The shape of the free surface is presented by curves which are found numerically by the series truncation method. This technique is based on the conformal transformations, resulting with the surface tension effect T with the boundary conditions on the free surfaces given by Bernoulli's equation. The found results are dependant on parameters which are: the Weber's number α and the angle γ. For each Weber's number value, only one solution is specified and some shapes of free surfaces of the jet are illustrated.

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