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Scopus Q: search.filters.scopusQuartile.Q1Subject: search.filters.subject.Adomian Decomposition Method

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Now showing 1 - 10 of 10
  • 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: 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.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 11
    Exact Solution for Nonlinear Local Fractional Partial Differential Equations
    (Shahid Chamran Univ Ahvaz, Iran, 2020) Cherif, Mountassir Hamdi; Baleanu, Dumitru; Belghaba, Kacem; Ziane, Djelloul
    In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples and the results obtained, showed the flexibility of applying this algorithm, and therefore, it can be applied to similar examples.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 56
    Exact Solution of Two-Dimensional Fractional Partial Differential Equations
    (Mdpi, 2020) Jassim, Hassan Kamil; Baleanu, Dumitru
    In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 7
    An Approximate-Analytical Solution To Analyze Fractional View of Telegraph Equations
    (Ieee-inst Electrical Electronics Engineers inc, 2020) Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Ali, Izaz
    In the present research article, a modified analytical method is applied to solve time-fractional telegraph equations. The Caputo-operator is used to express the derivative of fractional-order. The present method is the combination of two well-known methods namely Mohan transformation method and Adomian decomposition method. The validity of the proposed technique is confirmed through illustrative examples. It is observed that the obtained solutions have strong contact with the exact solution of the examples. Moreover, it is investigated that the present method has the desired degree of accuracy and provided the graphs closed form solutions of all targeted examples. The graphs have verified the convergence analysis of fractional-order solutions to integer-order solution. In conclusion, the suggested method is simple, straightforward and an effective technique to solve fractional-order partial differential equations.
  • Article
    Citation - WoS: 211
    Citation - Scopus: 242
    Chaos Analysis and Asymptotic Stability of Generalized Caputo Fractional Differential Equations
    (Pergamon-elsevier Science Ltd, 2017) Wu, Guo-Cheng; Zeng, Sheng-Da; Baleanu, Dumitru
    This paper investigates chaotic behavior and stability of fractional differential equations within a new generalized Caputo derivative. A semi-analytical method is proposed based on Adomian polynomials and a fractional Taylor series. Furthermore, chaotic behavior of a fractional Lorenz equation are numerically discussed. Since the fractional derivative includes two fractional parameters, chaos becomes more complicated than the one in Caputo fractional differential equations. Finally, Lyapunov stability is defined for the generalized fractional system. A sufficient condition of asymptotic stability is given and numerical results support the theoretical analysis. (C) Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 16
    Approximate Solutions To the Conformable Rosenau-Hyman Equation Using the Two-Step Adomian Decomposition Method With Pade Approximation
    (Wiley, 2020) Aliyu, Aliyu Isa; Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Akgul, Ali
    This paper adopts the Adomian decomposition method and the Pade approximation techniques to derive the approximate solutions of a conformable Rosenau-Hyman equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing both the analytic and approximate solutions.