Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 9Citation - Scopus: 12Two-Wave, Breather Wave Solutions and Stability Analysis To the (2+1)-Dimensional Ito Equation(Elsevier, 2022) Yusuf, Abdullahi; Hincal, Evren; Baleanu, Dumitru; Bayram, Mustafa; Sulaiman, Tukur AbdulkadirThe current study employs the novel Hirota bilinear scheme to investigate the nonlinear model. Thus, we acquire some two-wave and breather wave solutions to the governing equation. Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process. Several recent investigations, on the other hand, imply that breathers can survive in more complex habitats, such as random seas, despite the attributed phys-ical restrictions. The authenticity and genuineness of all the acquired solutions agreed with the original equation. In order to shed more light on these novel solutions, we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values. The governing model is also stable because of the idea of linear stability. The study's findings may help explain the physics behind some of the chal-lenges facing ocean engineers.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )Article Citation - WoS: 14Citation - Scopus: 15Lump, Its Interaction Phenomena and Conservation Laws To a Nonlinear Mathematical Model(Elsevier, 2022) Sulaiman, Tukur Abdulkadir; Hincal, Evren; Baleanu, Dumitru; Yusuf, AbdullahiWe solve the Ostrovsky equation in the absence of the rotation effect using the Hirota bilinear method and symbolic calculation. Some unique interaction phenomena have been obtained between lump so-lution, breather wave, periodic wave, kink soliton, and two-wave solutions. All the obtained solutions are validated by putting them into the original problem using the Wolfram Mathematica 12. The physical characteristics of the solutions have been visually represented to shed additional light on the acquired re-sults. Furthermore, using the novel conservation theory, the conserved vectors of the governing equation have been generated. The discovered results are helpful in understanding particular physical phenomena in fluid dynamics as well as the dynamics of nonlinear higher dimensional wave fields in computational physics and ocean engineering and related disciplines.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )Article Citation - WoS: 37Citation - Scopus: 45An Effective Computational Method To Deal With a Time-Fractional Nonlinear Water Wave Equation in the Caputo Sense(Elsevier, 2021) Ilie, Mousa; Mirzazadeh, Mohammad; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadir; Baleanu, Dumitru; Salahshour, Soheil; Hosseini, KamyarThe authors' concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new analytical method based on the Laplace transform and the homotopy analysis method to the governing model and obtaining its approximate solutions in the presence of the Caputo fractional derivative. To analyze the influence of the Caputo operator on the dynamical behavior of the approximate solutions, some graphical illustrations in two- and three-dimensions are formally presented. Furthermore, several numerical tables are given to support the performance of the new analytical method in handling the time-fractional nonlinear water wave equation. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.Article Citation - WoS: 125Citation - Scopus: 137A New Fractional Hrsv Model and Its Optimal Control: A Non-Singular Operator Approach(Elsevier, 2020) Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa; Jajarmi, AminIn the current work, a fractional version of SIRS model is extensively investigated for the HRSV disease involving a new derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The fixed-point theory is employed to show the existence and uniqueness of the solution for the model under consideration. In order to see the performance of this model, simulation and comparative analyses are carried out according to the real experimental data from the state of Florida. To believe upon the results obtained, the fractional order is allowed to vary between (0, 1) whereupon the physical observations show that the fractional dynamical character depends on the order of derivative operator and approaches an integer solution as a tends to 1. These features make the model more applicable when presented in the structure of fractional-order with ABC derivative. The effect of treatment by an optimal control strategy is also examined on the evolution of susceptible, infectious, and recovered individuals. Simulation results indicate that our fractional modeling and optimal control scheme are less costly and more effective than the proposed approach in the classical version of the model to diminish the HRSV infected individuals. (C) 2019 Elsevier B.V. All rights reserved.Article Citation - WoS: 63Citation - Scopus: 71Lie Symmetry Analysis, Explicit Solutions and Conservation Laws for the Space-Time Fractional Nonlinear Evolution Equations(Elsevier, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, MustafaThis paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations. Some interesting figures for the obtained explicit solutions are presented. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 111Citation - Scopus: 113Lie Symmetry Analysis, Exact Solutions and Conservation Laws for the Time Fractional Caudrey-Dodd Equation(Elsevier, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 39Citation - Scopus: 49Investigation of the Logarithmic-Kdv Equation Involving Mittag-Leffler Type Kernel With Atangana-Baleanu Derivative(Elsevier, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, MustafaThis work presents analysis of the logarithmic-KdV equation involving new fractional operator called Atangana-Baleanu (AB) fractional derivative with Mittag-Leffler (ML) type kernel. The existence and uniqueness of the governing equation having AB fractional derivative with ML type kernel is proved with the aid of a fixed-point theorem. We present numerical simulations by using iterative algorithm. The effectiveness of various parameters and variables on the displacement are presented in Figures 1 and 2. (C) 2018 Elsevier B.V. All rights reserved.