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A foundational approach to the Lie theory for fractional order partial differential equations

  • Rosario Antonio Leo EMAIL logo , Gabriele Sicuro und Piergiulio Tempesta
Veröffentlicht/Copyright: 19. Februar 2017
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Fractional Calculus and Applied Analysis
Aus der Zeitschrift Fractional Calculus and Applied Analysis Band 20 Heft 1

Abstract

We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie symmetries in the case of an arbitrary finite number of independent variables. We also prove the Lie theorem in the case of fractional differential equations, showing that the proper space for the analysis of these symmetries is the infinite dimensional jet space.

MSC 2010: Primary 26A33; Secondary 34A08; 34K37; 35R11; 76M60
Key Words and Phrases: fractional calculus; Riemann-Liouville fractional operator; fractional ordinary and partial differential equations; Lie theory; symmetries

Acknowledgments

G. S. acknowledges the financial support of the John Templeton Foundation. The research of P. T. has been partly supported by the research project FIS2015-63966, MINECO, Spain, and by the ICMAT Severo Ochoa project SEV-2015-0554 (MINECO).

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Received: 2016-3-16
Revised: 2016-11-12
Published Online: 2017-2-19
Published in Print: 2017-2-1

© 2017 Diogenes Co., Sofia

Artikel in diesem Heft

  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
https://doi.org/10.1515/fca-2017-0011
Schlagwörter für diesen Artikel
fractional calculus; Riemann-Liouville fractional operator; fractional ordinary and partial differential equations; Lie theory; symmetries

Artikel in diesem Heft

  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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