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Solution of linear fractional order systems with variable coefficients

  • Ivan Matychyn EMAIL logo and Viktoriia Onyshchenko
Published/Copyright: July 11, 2020
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 23 Issue 3

Abstract

The paper deals with the initial value problem for linear systems of FDEs with variable coefficients involving Riemann–Liouville derivatives. The technique of the generalized Peano–Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by an example.

MSC 2010: Primary 34A08; Secondary 49N05; 33E12
Key Words and Phrases: fractional differential equation; Riemann–Liouville fractional derivative; state transition matrix; generalized Peano–Baker series

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Received: 2019-06-27
Published Online: 2020-07-11
Published in Print: 2020-06-25

© 2020 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 23–3–2020)
  4. Survey Paper
  5. Why fractional derivatives with nonsingular kernels should not be used
  6. Fractional-order susceptible-infected model: Definition and applications to the study of COVID-19 main protease
  7. Generalized fractional Poisson process and related stochastic dynamics
  8. Research Paper
  9. Determination of the fractional order in semilinear subdiffusion equations
  10. Degenerate Kirchhoff (p, q)–Fractional systems with critical nonlinearities
  11. Solution of linear fractional order systems with variable coefficients
  12. “Fuzzy” calculus: The link between quantum mechanics and discrete fractional operators
  13. The green function for a class of Caputo fractional differential equations with a convection term
  14. Inverse problem for a multi-term fractional differential equation
  15. Maximum principles for a class of generalized time-fractional diffusion equations
  16. Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method
  17. Variational approximation for fractional Sturm–Liouville problem
  18. The 2-adic derivatives and fractal dimension of Takagi-like function on 2-series field
  19. Construction of fixed point operators for nonlinear difference equations of non integer order with impulses
  20. An averaging principle for stochastic differential equations of fractional order 0 < α < 1
  21. Weak solvability of the variable-order subdiffusion equation
https://doi.org/10.1515/fca-2020-0037
Keywords for this article
fractional differential equation; Riemann–Liouville fractional derivative; state transition matrix; generalized Peano–Baker series

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 23–3–2020)
  4. Survey Paper
  5. Why fractional derivatives with nonsingular kernels should not be used
  6. Fractional-order susceptible-infected model: Definition and applications to the study of COVID-19 main protease
  7. Generalized fractional Poisson process and related stochastic dynamics
  8. Research Paper
  9. Determination of the fractional order in semilinear subdiffusion equations
  10. Degenerate Kirchhoff (p, q)–Fractional systems with critical nonlinearities
  11. Solution of linear fractional order systems with variable coefficients
  12. “Fuzzy” calculus: The link between quantum mechanics and discrete fractional operators
  13. The green function for a class of Caputo fractional differential equations with a convection term
  14. Inverse problem for a multi-term fractional differential equation
  15. Maximum principles for a class of generalized time-fractional diffusion equations
  16. Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method
  17. Variational approximation for fractional Sturm–Liouville problem
  18. The 2-adic derivatives and fractal dimension of Takagi-like function on 2-series field
  19. Construction of fixed point operators for nonlinear difference equations of non integer order with impulses
  20. An averaging principle for stochastic differential equations of fractional order 0 < α < 1
  21. Weak solvability of the variable-order subdiffusion equation
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