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Null-controllability of a fractional order diffusion equation

  • Xiangdong Yang EMAIL logo
Published/Copyright: February 19, 2017
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 20 Issue 1

Abstract

The article considers the controllability of a fractional order diffusion equation. We show that the resulting fractional order diffusion equation is null-controllable. Our method reduces essentially to the study of a moment problem related to the Mittag-Leffler functions. Paley-Wiener type theorems are applied to construct biorthogonal sequence to a family of complex Mittag-Leffler functions.

MSC 2010: Primary 34A08, 30E05; Secondary 35E20, 41A75
Key Words and Phrases: null-controllability; Mittag-Leffler functions; Paley-Wiener type theorems; fractional order diffusion equation

Acknowledgements

The author thanks the editor and referees for suggestions that improved the original manuscript. The author also thanks National Natural Science Foundation of China for the support, under Grant No. 11261024.

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Received: 2016-3-14
Revised: 2016-11-29
Published Online: 2017-2-19
Published in Print: 2017-2-1

© 2017 Diogenes Co., Sofia

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https://doi.org/10.1515/fca-2017-0012
Keywords for this article
null-controllability; Mittag-Leffler functions; Paley-Wiener type theorems; fractional order diffusion equation

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 20–1–2017)
  4. Survey paper
  5. Ten equivalent definitions of the fractional laplace operator
  6. Research paper
  7. Consensus of fractional-order multi-agent systems with input time delay
  8. Research paper
  9. Asymptotic behavior of solutions of nonlinear fractional differential equations with Caputo-Type Hadamard derivatives
  10. Research paper
  11. A preconditioned fast finite difference method for space-time fractional partial differential equations
  12. Research paper
  13. On existence and uniqueness of solutions for semilinear fractional wave equations
  14. Research paper
  15. Computational solutions of the tempered fractional wave-diffusion equation
  16. Research paper
  17. Completeness on the stability criterion of fractional order LTI systems
  18. Research paper
  19. Wavelet convolution product involving fractional fourier transform
  20. Research paper
  21. Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method
  22. Research paper
  23. A foundational approach to the Lie theory for fractional order partial differential equations
  24. Research paper
  25. Null-controllability of a fractional order diffusion equation
  26. Research paper
  27. New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions
  28. Research paper
  29. The stretched exponential behavior and its underlying dynamics. The phenomenological approach
  30. Short Paper
  31. Lyapunov-type inequality for an anti-periodic fractional boundary value problem
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