Browsing by Author "Ali, Khalid K."

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Citation Count: Ali, Khalid K...et al. (2020). "Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model", Chaos Solitons & Fractals, Vol. 139.
Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model
(2020) Ali, Khalid K.; Cattani, Carlo; Gomez-Aguilar, J. F.; Baleanu, Dumitru; Osman, M. S.; 56389
In this work, we introduce a numerical and analytical study of the Peyrard-Bishop DNA dynamic model equation. This model is studied analytically by hyperbolic and exponential ansatz methods and numerically by finite difference method. A comparison between the results obtained by the analytical methods and the numerical method is investigated. Furthermore, some figures are introduced to show how accurate the solutions will be obtained from the analytical and numerical methods. (C) 2020 Elsevier Ltd. All rights reserved.
Citation Count: Park, Choonkil...et al. (2020). "Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg-de Vries equations". ADVANCES IN DIFFERENCE EQUATIONS. Vol: 2020, No: 1.
Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg-de Vries equations
(2020) Park, Choonkil; Nuruddeen, R., I; Ali, Khalid K.; Muhammad, Lawal; Osman, M. S.; Baleanu, Dumitru; 56389
This paper aims to investigate the class of fifth-order Korteweg-de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.
Citation Count: Nisar, Kottakkaran Sooppy...et al. (2022). "On beta-time fractional biological population model with abundant solitary wave structures", Alexandria Engineering Journal, Vol. 61, No. 3, pp. 1996-2008.
On beta-time fractional biological population model with abundant solitary wave structures
(2022) Nisar, Kottakkaran Sooppy; Ciancio, Armando; Ali, Khalid K.; Osman, M.S.; Cattani, Carlo; Baleanu, Dumitru; Zafar, Asim; Raheel, M.; Azeem, M.; 56389
The ongoing study deals with various forms of solutions for the biological population model with a novel beta-time derivative operators. This model is very conducive to explain the enlargement of viruses, parasites and diseases. This configuration of the aforesaid classical scheme is scouted for its new solutions especially in soliton shape via two of the well known analytical strategies, namely: the extended Sinh-Gordon equation expansion method (EShGEEM) and the Expa function method. These soliton solutions suggest that these methods have widened the scope for generating solitary waves and other solutions of fractional differential equations. Different types of soliton solutions will be gained such as dark, bright and singular solitons solutions with certain conditions. Furthermore, the obtained results can also be used in describing the biological population model in some better way. The numerical solution for the model is obtained using the finite difference method. The numerical simulations of some selected results are also given through their physical explanations. To the best of our knowledge, No previous literature discussed this model through the application of the EShGEEM and the Expa function method and supported their new obtained results by numerical analysis.
Citation Count: Almusawa, Hassan...et al. (2021). "Protracted study on a real physical phenomenon generated by media inhomogeneities", Results in Physics, Vol. 31.
Protracted study on a real physical phenomenon generated by media inhomogeneities
(2021) Almusawa, Hassan; Ali, Khalid K.; Wazwaz, Abdul-Majid; Mehanna, M.S.; Baleanu, Dumitru; Osman, M.S.; 56389
In this work, we study the dynamical behavior for a real physical application due to the inhomogeneities of media via analytical and numerical approaches. This phenomenon is described by the 3D Date–Jimbo–Kashiwara–Miwa (3D-DJKM) equation. For analytical techniques, three different methods are performed to get hyperbolic, trigonometric and rational functions solutions. After that, the obtained solutions are graphically depicted through 2D- and 3D-plots and numerically compared via the finite difference algorithm to check the precision of the proposed methods.
Citation Count: Alharthi, Mohammed Shaaf...et.al. (2022). "The dynamical behavior for a famous class of evolution equations with double exponential nonlinearities", Journal of Ocean Engineering and Science, pp.1-7.
The dynamical behavior for a famous class of evolution equations with double exponential nonlinearities
(2022) Alharthi, Mohammed Shaaf; Baleanu, Dumitru; Ali, Khalid K.; Nuruddeen, R.I.; Muhammad, Lawal; Aljohani, Abdulrahman F.; Osman, M.S.; 56389
An analytical investigation for a famous class of evolution equations with double exponential nonlinearities that has vast applications in many nonlinear sciences is presented. These equations include the Tzitzéica Equation (TE), Dodd-Bullough-Mikhailov Equation (DBME), Tzitzéica-Dodd-Bullough-Mikhailov equation (TDBME) and the Peyrard Bishop DNA Equation (PB-DNA-E). Furthermore, the Kudryashov method for constructing exponential function solutions has been employed to reveal various sets of traveling wave solutions with different geometrical structures to the identified models. We also give the graphical illustrations of certain solutions to further analyze the results.
Citation Count: Ali, Khalid K.;...et.al. (2023). "The nonlocal coupled system of Caputo–Fabrizio fractional q-integro differential equation", Mathematical Methods in the Applied Sciences.
The nonlocal coupled system of Caputo–Fabrizio fractional q-integro differential equation
(2023) Ali, Khalid K.; Raslan, K.R.; Ibrahim, Amira Abd-Elall; Baleanu, Dumitru; 56389
This scheme's main goal is to examine the existence, uniqueness, and continuous dependence of solutions for a nonlinear coupled system of fractional q-integro-differential equations involving the derivation and integration of fractional Caputo–Fabrizio. The numerical technique methodology of the proposed problem will be introduced. Proving the existence theorem depends on Schauder's fixed-point theorem. To drive the numerical method, we use the definitions of the fractional derivative and integral of Caputo–Fabrizio and the q-integral of the Riemann–Liouville type. Then, the integral part will be treated using the trapezoidal method, and the derivative part will be treated using the forward finite difference method. And therefore, the coupled system will be converted into a system of algebraic equation that will be solved together to get the solutions. Finally, we give two examples to illustrate the effectiveness of the suggested approach.