Aden Ahmed

Bio: Aden Ahmed is an academic researcher. The author has contributed to research in topics: Homotopy analysis method & Hamilton–Jacobi–Bellman equation. The author has an hindex of 1, co-authored 1 publications receiving 5 citations.

On the hamilton–jacobi–bellman equation by the homotopy perturbation method

Abstract: Our concern in this paper is to use the homotopy decomposition method to solve the Hamilton-Jacobi-Bellman equation (HJB). The approach is obviously extremely well organized and is an influential procedure in obtaining the solutions of the equations. We portrayed particular compensations that this technique has over the prevailing approaches. We presented that the complexity of the homotopy decomposition method is of order . Furthermore, three explanatory examples established good outcomes and comparisons with exact solution.

Various generalizations of metric spaces and fixed point theorems

Abstract: There have been many attempts to generalize the definition of a metric space in order to obtain possibilities for more general fixed point results. In this paper, we give a survey of recent results on reducing fixed point theorems on generalized metric spaces to fixed point theorems on metric spaces and then investigate this fact in other generalized metric spaces. We show that many generalized metric spaces are topologically equivalent to certain metric spaces or to previously generalized metric spaces. Also, the fixed point theory in these generalized metric spaces may be a consequence of the fixed point theory in certain metric spaces or in previously generalized metric spaces.

On the Solitary Wave Solutions to the (2+1)-Dimensional Davey-Stewartson Equations

Abstract: In this article, by using the Bernoulli sub-equation, we build the analytical traveling wave solution of the (2+1)-dimensional Davey-Stewartson equation system. First of all, the imaginary (2+1)-dimensional Davey-Stewatson system is transformed into a system of nonlinear differential equations, After getting the resultant equation, the homogeneous method of balance between the highest power and the highest derivative of the ordinary differential equation is authorized and finally the outcomes equations are solved in order to achieve some new analytical solutions. Wolfram Mathematica Package is used for different cases as well as for different values of constants to investigate the solutions of the resulting system of a nonlinear differential equation. The results of this study are shown in 2D and 3D dimensions graphically.

W-shaped soliton solutions to the modified Zakharov-Kuznetsov equation of ion-acoustic waves in (3+1)-dimensions arise in a magnetized plasma

Abstract: This paper is presented to investigate the exact solutions to the modified Zakharov-Kuznetsov equation that have a critical role to play in mathematical physics. The $ \tan \left(\phi \left(\zeta \right)/2 \right) $-expansion, $ (m+G'(\zeta)/G(\zeta)) $-expansion and He exponential function methods are used to reveal various analytical solutions of the model. The equation regulates the treatment of weakly nonlinear ion-acoustic waves in a plasma consisting of cold ions and hot isothermal electrons throughout the existence of a uniform magnetic field. Solutions in forms of W-shaped, singular, periodic-bright and bright are constructed.