Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Khan, Hassan

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  • Article
    The Analytical Analysis of Time-Fractional Fornberg-Whitham Equations
    (MDPI AG, 2020) Baleanu, Dumitru; Shah, Rasool; Aly, Shaban; Khan, Hassan; Alderremy, A.A.
  • Article
    Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay
    (MDPI AG, 2019) Baleanu, Dumitru; Shah, Rasool; Arif, Muhammad; Khan, Hassan; Kumam, Poom
  • Article
    A Novel Fractional Case Study of Nonlinear Dynamics Via Analytical Approach
    (Zhejiang Univ Press, 2024) Khan, Hassan; Khan, Adnan; Shah, Rasool; Baleanu, Dumitru
    The 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: 49
    Citation - Scopus: 61
    Laplace Decomposition for Solving Nonlinear System of Fractional Order Partial Differential Equations
    (Springer, 2020) Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; Khan, Hassan
    In 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: 37
    Citation - Scopus: 48
    An 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; Hajira
    In 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: 36
    Citation - Scopus: 35
    Travelling Waves Solution for Fractional-Order Biological Population Model
    (Edp Sciences S A, 2021) Shah, Rasool; Gomez-Aguilar, J. F.; Shoaib; Baleanu, Dumitru; Kumam, Poom; Khan, Hassan
    In this paper, we implemented the generalized (G'/G) and extended (G'/G) methods to solve fractional-order biological population models. The fractional-order derivatives are represented by the Caputo operator. The solutions of some illustrative examples are presented to show the validity of the proposed method. First, the transformation is used to reduce the given problem into ordinary differential equations. The ordinary differential equation is than solve by using modified (G'/G) method. Different families of traveling waves solutions are constructed to explain the different physical behavior of the targeted problems. Three important solutions, hyperbolic, rational and periodic, are investigated by using the proposed techniques. The obtained solutions within different classes have provided effective information about the targeted physical procedures. In conclusion, the present techniques are considered the best tools to analyze different families of solutions for any fractional-order problem.
  • Article
    Citation - WoS: 37
    Citation - Scopus: 40
    The Analytical Investigation of Time-Fractional Multi-Dimensional Navier-Stokes Equation
    (Elsevier, 2020) Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, Rasool
    In the present research article, we implemented two well-known analytical techniques to solve fractional-order multi-dimensional Navier-Stokes equation. The proposed methods are the modification of Adomian decomposition method and variational iteration method by using natural transformation. Furthermore, some illustrative examples are presented to confirm the validity of the suggested methods. The solutions graphs and tables are constructed for both fractional and integer-order problems. It is investigated that the suggested techniques have the identical solutions of the problems. The solution comparison via graphs and tables have also supported the greater accuracy and higher rate of convergence of the present methods. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 17
    The 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, Jiabin
    The 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, Dumitru
    The 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: 4
    Citation - Scopus: 4
    On 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, Hassan
    In 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.