Scopus İndeksli Yayınlar Koleksiyonu

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

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Subject: search.filters.subject.Adomian Decomposition Method

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Now showing 1 - 10 of 21
  • 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
    Exact Solution for Nonlinear Local Fractional Partial Differential Equations
    (Shahid Chamran University of Ahvaz, 2020) Ziane, Djelloul; Baleanu, Dumitru; Cherif, Mountassir Hamdi; Belghaba, Kacem
  • Article
    Citation - WoS: 105
    Citation - Scopus: 111
    Approximate Solutions for Diffusion Equations on Cantor Space-Time
    (Editura Acad Romane, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Zhong, Wei-Ping; Matematik
    In this paper we investigate diffusion equations on Cantor space-time and we obtain approximate solutions by using the local fractional Adomian decomposition method derived from the local fractional operators. Analytical solutions are given in terms of the Mittag-Leffler functions defined on Cantor sets.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 18
    Strong Interaction of Jafari Decomposition Method With Nonlinear Fractional-Order Partial Differential Equations Arising in Plasma Via the Singular and Nonsingular Kernels
    (Amer inst Mathematical Sciences-aims, 2022) Ashraf, Rehana; Jarad, Fahd; Rashid, Saima
    This research utilizes the Jafari transform and the Adomian decomposition method to derive a fascinating explicit pattern for the outcomes of the KdV, mKdV, K(2,2) and K(3,3) models that involve the Caputo fractional derivative operator and the Atangana-Baleanu fractional derivative operator in the Caputo sense. The novel exact-approximate solutions are derived from the formulation of trigonometric, hyperbolic, and exponential function forms. Laser and plasma sciences may benefit from these solutions. It is demonstrated that this approach produces a simple and effective mathematical framework for tackling nonlinear problems. To provide additional context for these ideas, simulations are performed, employing a computationally packaged program to assist in comprehending the implications of solutions.
  • 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: 4
    Citation - Scopus: 4
    A Novel Formulation of the Fuzzy Hybrid Transform for Dealing Nonlinear Partial Differential Equations Via Fuzzy Fractional Derivative Involving General Order
    (Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S. K.; Alqurashi, M. S.
    The main objective of the investigation is to broaden the description of Caputo fractional derivatives (in short, CFDs) (of order 0 < alpha < r) considering all relevant permutations of entities involving t(1) equal to 1 and t(2) (the others) equal to 2 via fuzz Under gH-differentiability, we also construct fuzzy Elzaki transforms for CFDs for the generic fractional order alpha is an element of (r - 1, r). Furthermore, a novel decomposition method for obtaining the solutions to nonlinear fuzzy fractional partial differential equations (PDEs) via the fuzzy Elzaki transform is constructed. The aforesaid scheme is a novel correlation of the fuzzy Elzaki transform and the Adorn ian decomposition method. In terms of CFD, several new results for the general fractional order are obtained via gH-differentiability. By considering the triangular fuzzy numbers of a nonlinear fuzzy fractional PDE, the correctness and capabilities of the proposed algorithm are demonstrated. In the domain of fractional sense, the schematic representation and tabulated outcomes indicate that the algorithm technique is precise and straightforward. Subsequently, future directions and concluding remarks are acted upon with the most focused use of references.
  • 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.