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Fractional Sturm–Liouville equations : self-adjoint extensions

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Abstract
In this report we study a fractional analogue of Sturm-Liouville equation. A class of self-adjoint fractional Sturm-Liouville operators is described. We give a biological interpretation of the fractional order equation and nonlocal boundary conditions that arise in describing the systems separated by a membrane. In particular, the connection with so called fractional kinetic equations is observed. Also, some spectral properties of the fractional kinetic equations are derived. An application to the anomalous diffusion of particles in a heterogeneous system of the fractional Sturm-Liouville equations is discussed.
Keywords
Computational Theory and Mathematics, Applied Mathematics, Computational Mathematics, Fractional kinetic equation, Caputo derivative, Riemann-Liouville derivative, Green's formula, Self-adjoint problem, Conservation law, The extension theory

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MLA
Tokmagambetov, Niyaz, and Berikbol Torebek. “Fractional Sturm–Liouville Equations : Self-Adjoint Extensions.” COMPLEX ANALYSIS AND OPERATOR THEORY, vol. 13, no. 5, 2019, pp. 2259–67, doi:10.1007/s11785-018-0828-z.
APA
Tokmagambetov, N., & Torebek, B. (2019). Fractional Sturm–Liouville equations : self-adjoint extensions. COMPLEX ANALYSIS AND OPERATOR THEORY, 13(5), 2259–2267. https://doi.org/10.1007/s11785-018-0828-z
Chicago author-date
Tokmagambetov, Niyaz, and Berikbol Torebek. 2019. “Fractional Sturm–Liouville Equations : Self-Adjoint Extensions.” COMPLEX ANALYSIS AND OPERATOR THEORY 13 (5): 2259–67. https://doi.org/10.1007/s11785-018-0828-z.
Chicago author-date (all authors)
Tokmagambetov, Niyaz, and Berikbol Torebek. 2019. “Fractional Sturm–Liouville Equations : Self-Adjoint Extensions.” COMPLEX ANALYSIS AND OPERATOR THEORY 13 (5): 2259–2267. doi:10.1007/s11785-018-0828-z.
Vancouver
1.
Tokmagambetov N, Torebek B. Fractional Sturm–Liouville equations : self-adjoint extensions. COMPLEX ANALYSIS AND OPERATOR THEORY. 2019;13(5):2259–67.
IEEE
[1]
N. Tokmagambetov and B. Torebek, “Fractional Sturm–Liouville equations : self-adjoint extensions,” COMPLEX ANALYSIS AND OPERATOR THEORY, vol. 13, no. 5, pp. 2259–2267, 2019.
@article{8662794,
  abstract     = {{In this report we study a fractional analogue of Sturm-Liouville equation. A class of self-adjoint fractional Sturm-Liouville operators is described. We give a biological interpretation of the fractional order equation and nonlocal boundary conditions that arise in describing the systems separated by a membrane. In particular, the connection with so called fractional kinetic equations is observed. Also, some spectral properties of the fractional kinetic equations are derived. An application to the anomalous diffusion of particles in a heterogeneous system of the fractional Sturm-Liouville equations is discussed.}},
  author       = {{Tokmagambetov, Niyaz and Torebek, Berikbol}},
  issn         = {{1661-8254}},
  journal      = {{COMPLEX ANALYSIS AND OPERATOR THEORY}},
  keywords     = {{Computational Theory and Mathematics,Applied Mathematics,Computational Mathematics,Fractional kinetic equation,Caputo derivative,Riemann-Liouville derivative,Green's formula,Self-adjoint problem,Conservation law,The extension theory}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{2259--2267}},
  title        = {{Fractional Sturm–Liouville equations : self-adjoint extensions}},
  url          = {{http://dx.doi.org/10.1007/s11785-018-0828-z}},
  volume       = {{13}},
  year         = {{2019}},
}

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