Browsing by Author "Osman M.S."

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A Variety of Novel Exact Solutions for Different Models With the Conformable Derivative in Shallow Water
(2020-06-16) Kumar D.; Kaplan M.; Haque M.R.; Osman M.S.; Baleanu D.
For different nonlinear time-conformable derivative models, a versatile built-in gadget, namely the generalized exp(−φ(ξ))-expansion (GEE) method, is devoted to retrieving different categories of new explicit solutions. These models include the time-fractional approximate long-wave equations, the time-fractional variant-Boussinesq equations, and the time-fractional Wu-Zhang system of equations. The GEE technique is investigated with the help of fractional complex transform and conformable derivative. As a result, we found four types of exact solutions involving hyperbolic function, periodic function, rational functional, and exponential function solutions. The physical significance of the explored solutions depends on the choice of arbitrary parameter values. Finally, we conclude that the GEE method is more effective in establishing the explicit new exact solutions than the exp(−φ(ξ))-expansion method.
Different Types of Progressive Wave Solutions via the 2D-Chiral Nonlinear Schrödinger Equation
(2020-07-07) Osman M.S.; Baleanu D.; Tariq K.U.H.; Kaplan M.; Younis M.; Rizvi S.T.R.
A versatile integration tool, namely the protracted (or extended) Fan sub-equation (PFS-E) technique, is devoted to retrieving a variety of solutions for different models in many fields of the sciences. This essay presents the dynamics of progressive wave solutions via the 2D-chiral nonlinear Schrödinger (2D-CNLS) equation. The solutions acquired comprise dark optical solitons, periodic solitons, singular dark (bright) solitons, and singular periodic solutions. By comparing the results gained in this work with other literature, it can be noticed that the PFS-E method is an useful technique for finding solutions to other similar problems. Furthermore, some new types of solutions are revealed that will help us better understand the dynamic behaviors of the 2D-CNLS model.
On the conservation laws and exact solutions to the (3+1)-dimensional modified kdv-zakharov-kuznetsov equation
(2021-05-01) Akbulut A.; Almusawa H.; Kaplan M.; Osman M.S.
In this paper, we consider conservation laws and exact solutions of the (3+1)-dimensional modified KdV–Zakharov–Kuznetsov equation. Firstly, we construct conservation laws of the given equation with the help of the conservation theorem; the developed conservation laws are modified conservation laws. Then, we obtain exact solutions of the given equation via the (G′ /G, 1/G)-expansion method. The obtained solutions are classified as trigonometric solutions, hyperbolic solutions and rational solutions. Furthermore, graphical representations of the obtained solutions are given.