Browsing by Author "Akbar, M. Ali"

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Citation - WoS: 31
Citation - Scopus: 28
Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation
(Elsevier, 2020) Barman, Hemonta Kumar; Baleanu, Dumitru; Seadawy, Aly R.; Akbar, M. Ali; Baleanu, Dumitru; 56389; Matematik
The Riemann wave equation and the Novikov-Veselov equation are interesting nonlinear equations in the sphere of tidal and tsunami waves in ocean, river, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and stationary media etc. In this article, the generalized Kudryashov method is executed to demonstrate the applicability and effectiveness to extract travelling and solitary wave solutions of higher order nonlinear evolution equations (NLEEs) via the earlier stated equations. The technique is enucleated to extract solitary wave solutions in terms of trigonometric, hyperbolic and exponential function. We acquire bell shape soliton, consolidated bell shape soliton, compacton, singular kink soliton, flat kink shape soliton, smooth singular soliton and other types of soliton solutions by setting particular values of the embodied parameters. For the precision of the result, the solutions are graphically illustrated in 3D and 2D. The analytic solutions greatly facilitate the verification of numerical solvers on the stability analysis of the solution.
Citation - WoS: 1
Citation - Scopus: 4
Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics
(Wiley, 2022) Siddique, Imran; Jarad, Fahd; Mirza, Arshad M.; Shahzadi, Kausar; Akbar, M. Ali; Jarad, Fahd; 234808; Matematik
In this paper, we obtain the novel exact traveling wave solutions in the form of trigonometric, hyperbolic and exponential functions for the nonlinear time fractional generalized reaction Duffing model and density dependent fractional diffusion-reaction equation in the sense of beta-derivative by using three fertile methods, namely, Generalized tanh (GT) method, Generalized Bernoulli (GB) sub-ODE method, and Riccati-Bernoulli (RB) sub-ODE method. The derived solutions to the aforementioned equations are validated through symbolic soft computations. To promote the vital propagated features; some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the specific values to the parameters under the confine conditions. The accomplished solutions show that the presented methods are not only powerful mathematical tools for generating more solutions of nonlinear time fractional partial differential equations but also can be applied to nonlinear space-time fractional partial differential equations.
Citation - WoS: 21
Citation - Scopus: 24
Explicit wave phenomena to the couple type fractional order nonlinear evolution equations
(Elsevier, 2021) Khatun, M. Ayesha; Baleanu, Dumitru; Arefin, Mohammad Asif; Uddin, M. Hafiz; Baleanu, Dumitru; Akbar, M. Ali; Inc, Mustafa; 56389; Matematik
We utilize the fractional modified Riemann-Liouville derivative in the sense to develop careful arrangements of space-time fractional coupled Boussinesq equation which emerges in genuine applications, for instance, nonlinear framework waves iron sound waves in plasma and in vibrations in nonlinear string and space-time fractional-coupled Boussinesq Burger equation that emerges in the investigation of liquids stream in a dynamic framework and depicts engendering of shallow-water waves. A decent comprehension of its solutions is exceptionally useful for beachfront and engineers to apply the nonlinear water wave model to the harbor and seaside plans. A summed-up partial complex transformation is correctly used to change this equation to a standard differential equation thus, many precise logical arrangements are acquired with all the free parameters. At this point, the traveling wave arrangements are articulated by hyperbolic functions, trigonometric functions, and rational functions, if these free parameters are considered as specific values. We obtain kink wave solution, periodic solutions, singular kink type solution, and anti-kink type solutions which are shown in 3D and contour plots. The presentation of the method is dependable and important and gives even more new broad accurate arrangements.
Citation - WoS: 31
Citation - Scopus: 36
Physically significant wave solutions to the Riemann wave equations and the Landau-Ginsburg-Higgs equation
(Elsevier, 2021) Barman, Hemonta Kumar; Baleanu, Dumitru; Aktar, Most Shewly; Uddin, M. Hafiz; Akbar, M. Ali; Baleanu, Dumitru; Osman, M. S.; 56389; Matematik
The nonlinear Riemann wave equations (RWEs) and the Landau-Ginsburg-Higgs (LGH) equation are related to plasma electrostatic waves, ion-cyclotron wave electrostatic potential, superconductivity, and drift coherent ioncyclotron waves in centrifugally inhomogeneous plasma. In this article, the interactions between the maximum order linear and nonlinear factors are balanced to compute realistic soliton solutions to the formerly stated equations in terms of hyperbolic functions. The linear and nonlinear effects rheostat the structure of the wave profiles, which vary in response to changes in the subjective parameters combined with the solutions. The established solutions to the aforementioned models using the extended tanh scheme are descriptive, typical, and consistent, and include standard soliton shapes such as bright soliton, dark soliton, compacton, peakon, periodic, and others that can be used to analyze in ion-acoustic and magneto-sound waves in plasma, homogeneous, and stationary media, particularly in the propagation of tidal and tsunami waves.