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Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

  • Mohamed M. Khader EMAIL logo
Published/Copyright: September 23, 2020
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 22 Issue 1

Abstract

This paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

Keywords: Adams-Bashforth-Moulton method; convergence order; variable-order fractional Riccati and Logistic differential equations
Corresponding author: Mohamed M. Khader, Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt; and Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia,

Acknowledgments

The author is very grateful to the editor and referees for carefully reading the paper and for their comments and suggestions which have improved the paper.

  1. Authors contributions: The paper has one author.

  2. Research funding: Not applicable.

  3. Conflict of interests: The author declares that there is no conflict of interests regarding the publication of this paper.

  4. Availability of data and materials: Not applicable.

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Received: 2019-12-20
Accepted: 2020-08-08
Published Online: 2020-09-23
Published in Print: 2021-02-23

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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  1. Frontmatter
  2. Original Research Articles
  3. Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control
  4. Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays
  5. The monotone iterative method for the integral boundary value problems of fractional p-Laplacian equations with delay
  6. Solvability of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators
  7. Synchronization of Cohen-Grossberg fuzzy cellular neural networks with time-varying delays
  8. Application of Hermite–Padé approximation for detecting singularities of some boundary value problems
  9. The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs
  10. A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument
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https://doi.org/10.1515/ijnsns-2019-0307
Keywords for this article
Adams-Bashforth-Moulton method; convergence order; variable-order fractional Riccati and Logistic differential equations

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control
  4. Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays
  5. The monotone iterative method for the integral boundary value problems of fractional p-Laplacian equations with delay
  6. Solvability of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators
  7. Synchronization of Cohen-Grossberg fuzzy cellular neural networks with time-varying delays
  8. Application of Hermite–Padé approximation for detecting singularities of some boundary value problems
  9. The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs
  10. A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument
  11. Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models
  12. Synchronization stability on the BAM neural networks with mixed time delays
  13. Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method
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