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Periodic problem for two-term fractional differential equations

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Published/Copyright: June 22, 2017
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 20 Issue 3

Abstract

We discuss the existence, multiplicity and uniqueness of solutions to the periodic problem cDαu + q(t,u)cDβu = f(t,u), u(0) = u(T), where 0 < β < α ≤ 1. The existence results are proved by the combination of the Schauder fixed point theorem with the maximum principle for the Caputo fractional derivative and the structure of compact sets in ℝ.

MSC 2010: Primary 26A33; 34A08; Secondary 34C25; 33E12
Key Words and Phrases: two-term fractional differential equation; periodic problem; existence; multiplicity; uniqueness; maximum principle; Caputo fractional derivative; Basset fractional differential equation

Acknowledgements

Supported by the grant No. 14-06958S of the Grant Agency of the Czech Republic.

References

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Received: 2016-7-8
Published Online: 2017-6-22
Published in Print: 2017-6-27

© 2017 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 20–3–2017)
  4. Survey Paper
  5. A survey of useful inequalities in fractional calculus
  6. Survey Paper
  7. Non-instantaneous impulses in Caputo fractional differential equations
  8. Research Paper
  9. Analysis of two- and three-dimensional fractional-order Hindmarsh-Rose type neuronal models
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  11. Solvability of initial value problems with fractional order differential equations in banach spaces by α-dense curves
  12. Research Paper
  13. Periodic problem for two-term fractional differential equations
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  15. Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions
  16. Research Paper
  17. Identification problem for degenerate evolution equations of fractional order
  18. Research Paper
  19. Fractional-compact numerical algorithms for Riesz spatial fractional reaction-dispersion equations
  20. Research Paper
  21. Impact of fractional order methods on optimized tilt control for rail vehicles
  22. Historical Survey
  23. Life and science of Alexey Gerasimov, one of the pioneers of fractional calculus in Soviet union
  24. Short Paper
  25. Regular fractional differential equations in the Sobolev space
  26. Short Paper
  27. Monotonicity and convexity results for a function through its Caputo fractional derivative
https://doi.org/10.1515/fca-2017-0035
Keywords for this article
two-term fractional differential equation; periodic problem; existence; multiplicity; uniqueness; maximum principle; Caputo fractional derivative; Basset fractional differential equation

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 20–3–2017)
  4. Survey Paper
  5. A survey of useful inequalities in fractional calculus
  6. Survey Paper
  7. Non-instantaneous impulses in Caputo fractional differential equations
  8. Research Paper
  9. Analysis of two- and three-dimensional fractional-order Hindmarsh-Rose type neuronal models
  10. Research Paper
  11. Solvability of initial value problems with fractional order differential equations in banach spaces by α-dense curves
  12. Research Paper
  13. Periodic problem for two-term fractional differential equations
  14. Research Paper
  15. Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions
  16. Research Paper
  17. Identification problem for degenerate evolution equations of fractional order
  18. Research Paper
  19. Fractional-compact numerical algorithms for Riesz spatial fractional reaction-dispersion equations
  20. Research Paper
  21. Impact of fractional order methods on optimized tilt control for rail vehicles
  22. Historical Survey
  23. Life and science of Alexey Gerasimov, one of the pioneers of fractional calculus in Soviet union
  24. Short Paper
  25. Regular fractional differential equations in the Sobolev space
  26. Short Paper
  27. Monotonicity and convexity results for a function through its Caputo fractional derivative
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