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Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method

  • Murat O. Mamchuev 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 inhomogeneous time-fractional telegraph equation with Caputo derivatives with constant coefficients is considered. For the considered equation, general representation of regular solution in rectangular domain is obtained and the fundamental solution is presented. Using this representation and the properties of the fundamental solution, the Cauchy problem and the main boundary value problems in half-strip and rectangular domains are studied. For the Cauchy problem theorems of existence and uniqueness of solution are proved, and the explicit form of the solution is constructed. The solutions of the investigated problems are constructed in terms of the appropriate Green functions, which are also constructed in explicit form.

MSC 2010: Primary 33R11; Secondary 35A08; 35A09; 35C05; 35C15; 35E05; 34A08
Key Words and Phrases: fractional telegraph equation; fractional diffussion-wave equation; fractional advection-dispersion equation; general representation of solution; fundamental solution; Cauchy problem; signalling problem; boundary value problems; Green functions

Acknowledgements

This work was partially supported by the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences, Project No. 5 Fundamental Problems and Technologies of Epitaxial Nanostructures and Devices Based on Them.

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Received: 2016-3-11
Revised: 2016-10-29
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-2017-0010
Keywords for this article
fractional telegraph equation; fractional diffussion-wave equation; fractional advection-dispersion equation; general representation of solution; fundamental solution; Cauchy problem; signalling problem; boundary value problems; Green functions

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
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  29. The stretched exponential behavior and its underlying dynamics. The phenomenological approach
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