WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article A Novel Fractional Case Study of Nonlinear Dynamics Via Analytical Approach(Zhejiang Univ Press, 2024) Khan, Hassan; Khan, Adnan; Shah, Rasool; Baleanu, DumitruThe present work describes the fractional view analysis of Newell-Whitehead-Segal equations, using an innovative technique. The work is carried with the help of the Caputo operator of fractional derivative. The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method. The derived results are very consistent with the actual solutions to the problems. A graphical representation has been done for the solution of the problems at various fractional-order derivatives. Moreover, the solution in series form has the desired rate of convergence and provides the closed-form solutions. It is noted that the procedure can be modified in other directions for fractional order problems.Article Citation - WoS: 49Citation - Scopus: 61Laplace Decomposition for Solving Nonlinear System of Fractional Order Partial Differential Equations(Springer, 2020) Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; Khan, HassanIn the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems.Article Citation - WoS: 37Citation - Scopus: 48An Approximate Analytical Solution of the Navier-Stokes Equations Within Caputo Operator and Elzaki Transform Decomposition Method(Springer, 2020) Khan, Hassan; Khan, Adnan; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; HajiraIn this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier-Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.Article Citation - WoS: 17Citation - Scopus: 17The Analytical Analysis of Nonlinear Fractional-Order Dynamical Models(Amer inst Mathematical Sciences-aims, 2021) Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; Xu, JiabinThe present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.Article The analytical analysis of nonlinear fractional-order dynamical models(Amer Inst Mathematical Sciences-AIMS, 2021) Xu, Jiabin; Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, DumitruThe present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.Article Citation - WoS: 4Citation - Scopus: 4On the Approximate Solution of Fractional-Order Whitham-Broer Equations(World Scientific Publ Co Pte Ltd, 2021) Gomez-Aguilar, J. F.; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; Khan, HassanIn this paper, the Homotopy perturbation Laplace method is implemented to investigate the solution of fractional-order Whitham-Broer-Kaup equations. The derivative of fractional-order is described in Caputo's sense. To show the reliability of the suggested method, the solution of certain illustrative examples are presented. The results of the suggested method are shown and explained with the help of its graphical representation. The solutions of fractional-order problems as well as integer-order problems are determined by using the present technique. It has been observed that the obtained solutions are in significant agreement with the actual solutions to the targeted problems. Computationally, it has been analyzed that the solutions at different fractional-orders have a higher rate of convergence to the solution at integer-order of the derivative. Due to the analytical analysis of the problems, this study can further modify the solution of other fractional-order problems.Article Citation - WoS: 16Citation - Scopus: 22New Approximate Analytical Technique for the Solution of Time Fractional Fluid Flow Models(Springer, 2021) Khan, Hassan; Tchier, Fairouz; Hincal, Evren; Baleanu, Dumitru; Bin Jebreen, Haifa; Farooq, Umar; Bin Jebreen, HaifaIn this note, we broaden the utilization of an efficient computational scheme called the approximate analytical method to obtain the solutions of fractional-order Navier-Stokes model. The approximate analytical solution is obtained within Liouville-Caputo operator. The analytical strategy generates the series form solution, with less computational work and fast convergence rate to the exact solutions. The obtained results have shown a simple and useful procedure to analyze complex problems in related areas of science and technology.Article Citation - WoS: 12Citation - Scopus: 10Fractional-Order Investigation of Diffusion Equations Via Analytical Approach(Frontiers Media Sa, 2021) Khan, Hassan; Mustafa, Saima; Mou, Lianming; Baleanu, Dumitru; Liu, HaobinThis research article is mainly concerned with the analytical solution of diffusion equations within a Caputo fractional-order derivative. The motivation and novelty behind the present work are the application of a sophisticated and straight forward procedure to solve diffusion equations containing a derivative of a fractional-order. The solutions of some illustrative examples are calculated to confirm the closed contact between the actual and the approximate solutions of the targeted problems. Through analysis it is shown that the proposed solution has a higher rate of convergence and provides a closed-form solution. The small number of calculations is the main advantage of the proposed method. Due to a comfortable and straight forward implementation, the suggested method can be utilized to nonlinear fractional-order problems in various applied science branches. It can be extended to solve other physical problems of fractional-order in multiple areas of applied sciences.Article Citation - WoS: 24Citation - Scopus: 25Modified Modelling for Heat Like Equations Within Caputo Operator(Mdpi, 2020) Khan, Adnan; Al-Qurashi, Maysaa; Shah, Rasool; Baleanu, Dumitru; Khan, HassanThe present paper is related to the analytical solutions of some heat like equations, using a novel approach with Caputo operator. The work is carried out mainly with the use of an effective and straight procedure of the Iterative Laplace transform method. The proposed method provides the series form solution that has the desired rate of convergence towards the exact solution of the problems. It is observed that the suggested method provides closed-form solutions. The reliability of the method is confirmed with the help of some illustrative examples. The graphical representation has been made for both fractional and integer-order solutions. Numerical solutions that are in close contact with the exact solutions to the problems are investigated. Moreover, the sample implementation of the present method supports the importance of the method to solve other fractional-order problems in sciences and engineering.Article Citation - WoS: 41Citation - Scopus: 47An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems(Mdpi, 2020) Khan, Adnan; Ali, Izaz; Al Qurashi, Maysaa; Khan, Hassan; Shah, Rasool; Baleanu, Dumitru; Qin, Ya; Qurashi, Maysaa AlMostly, it is very difficult to obtained the exact solution of fractional-order partial differential equations. However, semi-analytical or numerical methods are considered to be an alternative to handle the solutions of such complicated problems. To extend this idea, we used semi-analytical procedures which are mixtures of Laplace transform, Shehu transform and Homotopy perturbation techniques to solve certain systems with Caputo derivative differential equations. The effectiveness of the present technique is justified by taking some examples. The graphical representation of the obtained results have confirmed the significant association between the actual and derived solutions. It is also shown that the suggested method provides a higher rate of convergence with a very small number of calculations. The problems with derivatives of fractional-order are also solved by using the present method. The convergence behavior of the fractional-order solutions to an integer-order solution is observed. The convergence phenomena described a very broad concept of the physical problems. Due to simple and useful implementation, the current methods can be used to solve problems containing the derivative of a fractional-order.