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Non-local boundary value problem for the space degenerate partial differential equation

Erkinjon Karimov and Bakhodirjon Toshtemirov
(2022) International Scientific and Practical Conference : 'Modern problems of applied mathematics and information technologies', Proceedings. p.161-161
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Abstract
In this paper, we investigate the unique solvability of the non-local problem for the space- degenerate partial differential equation with bi-ordinal Hilfer fractional derivative. By using certain aspects of the equation and the properties of the Legendre polynomials the unique solution is constructed with help of the method of separation variables. The distinctive side of this work is that the uniqueness of the solution depends on the way of choosing the points in the non-local condition. Also, the conditions for given data are more specific than the considering general operator. Moreover, this work quite generalizes the Langevin-type equations with space variable and it might have some physical implementations.
Keywords
bi-ordinal Hilfer's derivative, boundary-value problems, fractional wave equation, hyper-Bessel fractional differential operator, sub-diffusion equation

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MLA
Karimov, Erkinjon, and Bakhodirjon Toshtemirov. “Non-Local Boundary Value Problem for the Space Degenerate Partial Differential Equation.” International Scientific and Practical Conference : “Modern Problems of Applied Mathematics and Information Technologies”, Proceedings, edited by Abdullo Hayotov, 2022, pp. 161–161.
APA
Karimov, E., & Toshtemirov, B. (2022). Non-local boundary value problem for the space degenerate partial differential equation. In A. Hayotov (Ed.), International Scientific and Practical Conference : “Modern problems of applied mathematics and information technologies”, Proceedings (pp. 161–161).
Chicago author-date
Karimov, Erkinjon, and Bakhodirjon Toshtemirov. 2022. “Non-Local Boundary Value Problem for the Space Degenerate Partial Differential Equation.” In International Scientific and Practical Conference : “Modern Problems of Applied Mathematics and Information Technologies”, Proceedings, edited by Abdullo Hayotov, 161–161.
Chicago author-date (all authors)
Karimov, Erkinjon, and Bakhodirjon Toshtemirov. 2022. “Non-Local Boundary Value Problem for the Space Degenerate Partial Differential Equation.” In International Scientific and Practical Conference : “Modern Problems of Applied Mathematics and Information Technologies”, Proceedings, ed by. Abdullo Hayotov, 161–161.
Vancouver
1.
Karimov E, Toshtemirov B. Non-local boundary value problem for the space degenerate partial differential equation. In: Hayotov A, editor. International Scientific and Practical Conference : “Modern problems of applied mathematics and information technologies”, Proceedings. 2022. p. 161–161.
IEEE
[1]
E. Karimov and B. Toshtemirov, “Non-local boundary value problem for the space degenerate partial differential equation,” in International Scientific and Practical Conference : “Modern problems of applied mathematics and information technologies”, Proceedings, Bukhara, 2022, pp. 161–161.
@inproceedings{8760719,
  abstract     = {{In this paper, we investigate the unique solvability of the non-local problem for the space-
degenerate partial differential equation with bi-ordinal Hilfer fractional derivative. By using certain
aspects of the equation and the properties of the Legendre polynomials the unique solution is constructed
with help of the method of separation variables. The distinctive side of this work is that the uniqueness of
the solution depends on the way of choosing the points in the non-local condition. Also, the conditions
for given data are more specific than the considering general operator. Moreover, this work quite
generalizes the Langevin-type equations with space variable and it might have some physical
implementations.}},
  author       = {{Karimov, Erkinjon and Toshtemirov, Bakhodirjon}},
  booktitle    = {{International Scientific and Practical Conference : 'Modern problems of applied mathematics and information technologies', Proceedings}},
  editor       = {{Hayotov, Abdullo}},
  keywords     = {{bi-ordinal Hilfer's derivative,boundary-value problems,fractional wave equation,hyper-Bessel fractional differential operator,sub-diffusion equation}},
  language     = {{eng,uzb,rus}},
  location     = {{Bukhara}},
  pages        = {{161--161}},
  title        = {{Non-local boundary value problem for the space degenerate partial differential equation}},
  year         = {{2022}},
}