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Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory

  • Hua Kong , Guo-Cheng Wu ORCID logo EMAIL logo , Hui Fu and Kai-Teng Wu
Published/Copyright: December 2, 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 3

Abstract

A new class of fractional differential equations with exponential memory was recently defined in the space A C δ n [ a , b ] . In order to use the famous predictor–corrector method, a new quasi-linear interpolation with a non-equidistant partition is suggested in this study. New Euler and Adams–Moulton methods are proposed for the fractional integral equation. Error estimates of the generalized fractional integral and numerical solutions are provided. The predictor–corrector method for the new fractional differential equation is developed and numerical solutions of fractional nonlinear relaxation equation are given. It can be concluded that the non-equidistant partition is needed for non-standard fractional differential equations.

Keywords: exponential memory; fractional calculus; non-equidistant partition; predictor–corrector
Corresponding author: Guo-Cheng Wu, Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China, E-mail:

Funding source: Innovation Team Project of Department of Education of Sichuan Province

Award Identifier / Grant number: 18TD0033

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 62076141

Acknowledgement

This work is financially supported by the National Natural Science Foundation of China (NSFC) (Grant No. 62076141), and Innovation Team Project of Department of Education of Sichuan Province (Grant No. 18TD0033).

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-06-09
Accepted: 2021-09-11
Published Online: 2021-12-02

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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  2. Original Research Articles
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  5. Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries
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  8. Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces
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  10. A new approach to representations of homothetic motions in Lorentz space
  11. Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics
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  17. Singularity analysis and analytic solutions for the Benney–Gjevik equations
  18. Trajectory controllability of nonlinear fractional Langevin systems
  19. Similarity transformations for modified shallow water equations with density dependence on the average temperature
  20. Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory
  21. Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction
  22. Dynamic response of Mathieu–Duffing oscillator with Caputo derivative
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https://doi.org/10.1515/ijnsns-2021-0232
Keywords for this article
exponential memory; fractional calculus; non-equidistant partition; predictor–corrector

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation
  4. Hopf bifurcations in a network of FitzHugh–Nagumo biological neurons
  5. Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries
  6. A new numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ equation
  7. Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems
  8. Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces
  9. Elastic trend filtering
  10. A new approach to representations of homothetic motions in Lorentz space
  11. Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics
  12. Stability analysis and numerical simulations of the fractional COVID-19 pandemic model
  13. Numerical solutions of the Bagley–Torvik equation by using generalized functions with fractional powers of Laguerre polynomials
  14. N-fold Darboux transformation and exact solutions for the nonlocal Fokas–Lenells equation on the vanishing and plane wave backgrounds
  15. Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations
  16. Master-slave synchronization in the Duffing-van der Pol and Φ6 Duffing oscillators
  17. Singularity analysis and analytic solutions for the Benney–Gjevik equations
  18. Trajectory controllability of nonlinear fractional Langevin systems
  19. Similarity transformations for modified shallow water equations with density dependence on the average temperature
  20. Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory
  21. Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction
  22. Dynamic response of Mathieu–Duffing oscillator with Caputo derivative
  23. Non-Newtonian fluid flow having fluid–particle interaction through a porous zone in a channel with permeable walls
  24. A class of computationally efficient Newton-like methods with frozen inverse operator for nonlinear systems
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