Startseite Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
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Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations

  • Boonrod Yuttanan , Mohsen Razzaghi und Thieu N. Vo EMAIL logo
Veröffentlicht/Copyright: 20. Mai 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
Aus der Zeitschrift International Journal of Nonlinear Sciences and Numerical Simulation Band 24 Heft 1

Abstract

In the present paper, fractional-order generalized Legendre wavelets (FOGLWs) are introduced. We apply the FOGLWs for solving fractional Riccati differential equation. By using the hypergeometric function, we obtain an exact formula for the Riemann–Liouville fractional integral operator (RLFIO) of the FOGLWs. By using this exact formula and the properties of the FOGLWs, we reduce the solution of the fractional Riccati differential equation to the solution of an algebraic system. This algebraic system can be solved effectively. This method gives very accurate results. The given numerical examples support this claim.

Keywords: fractional Riccati differential equation; fractional-order Legendre wavelet; hypergeometric function
Corresponding author: Thieu N. Vo, Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam, E-mail:

  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: 2020-06-22
Revised: 2021-02-11
Accepted: 2021-04-12
Published Online: 2021-05-20
Published in Print: 2023-02-23

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Modeling and assessment of the flow and air pollutants dispersion during chemical reactions from power plant activities
  4. Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
  5. Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
  6. Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
  7. Battery discharging model on fractal time sets
  8. Adaptive neural network control of second-order underactuated systems with prescribed performance constraints
  9. Optimal control for dengue eradication program under the media awareness effect
  10. Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations
  11. Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations
  12. Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis
  13. Anti-sway method for reducing vibrations on a tower crane structure
  14. Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized G ′ / G -expansion method
  15. Convergence analysis of online learning algorithm with two-stage step size
  16. An estimative (warning) model for recognition of pandemic nature of virus infections
  17. Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation
  18. Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications
  19. An efficient class of fourth-order derivative-free method for multiple-roots
  20. Numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
  21. Construction of breather solutions and N-soliton for the higher order dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns
  22. Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation
  23. Construction of complexiton-type solutions using bilinear form of Hirota-type
  24. Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization
  25. Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting
  26. Lump solutions to a generalized nonlinear PDE with four fourth-order terms
  27. Quantum motion control for packaging machines
https://doi.org/10.1515/ijnsns-2020-0137
Schlagwörter für diesen Artikel
fractional Riccati differential equation; fractional-order Legendre wavelet; hypergeometric function

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Modeling and assessment of the flow and air pollutants dispersion during chemical reactions from power plant activities
  4. Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
  5. Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
  6. Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
  7. Battery discharging model on fractal time sets
  8. Adaptive neural network control of second-order underactuated systems with prescribed performance constraints
  9. Optimal control for dengue eradication program under the media awareness effect
  10. Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations
  11. Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations
  12. Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis
  13. Anti-sway method for reducing vibrations on a tower crane structure
  14. Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized G ′ / G -expansion method
  15. Convergence analysis of online learning algorithm with two-stage step size
  16. An estimative (warning) model for recognition of pandemic nature of virus infections
  17. Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation
  18. Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications
  19. An efficient class of fourth-order derivative-free method for multiple-roots
  20. Numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
  21. Construction of breather solutions and N-soliton for the higher order dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns
  22. Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation
  23. Construction of complexiton-type solutions using bilinear form of Hirota-type
  24. Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization
  25. Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting
  26. Lump solutions to a generalized nonlinear PDE with four fourth-order terms
  27. Quantum motion control for packaging machines
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