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Matematicheskie Zametki, 2015, Volume 97, Issue 4, Pages 620–628
DOI: https://doi.org/10.4213/mzm8789 (Mi mzm8789) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Dirichlet Problem for Second-Order Ordinary Differential Equations with Segment-Order Derivative

B. I. Efendiev

Scientific Research Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Centre of the Russian Academy of Sciences
Full-text PDF (460 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm8789
Abstract: The fundamental solution of a second-order ordinary differential equation with segment-order derivative is constructed. The Green function of the Dirichlet problem is determined on the basis the fundamental solution and the solution of the Dirichlet problem for the equation under study is obtained under the solvability condition.
Keywords: second-order ordinary differential equation, Dirichlet problem, segment-order derivative, Green function, fundamental solution, Euler gamma function.
Funding agency Grant number
Russian Foundation for Basic Research 09-01-96510
This work was supported by the Russian Foundation for Basic Research (grant no. 09-01-96510).
Received: 10.12.2009
Revised: 20.01.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 4, Pages 632–640
DOI: https://doi.org/10.1134/S0001434615030347
Bibliographic databases:
Document Type: Article
UDC: 517.927.2
Language: Russian
Citation: B. I. Efendiev, “Dirichlet Problem for Second-Order Ordinary Differential Equations with Segment-Order Derivative”, Mat. Zametki, 97:4 (2015), 620–628; Math. Notes, 97:4 (2015), 632–640
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm8789
  • https://www.mathnet.ru/eng/mzm/v97/i4/p620
    • This publication is cited in the following 8 articles:
    1. Arsen V. Pskhu, “Inversion formulas for distributed order integration and differentiation operators”, J Math Sci, 2025  crossref
    2. Arsen Pskhu, “Transmutation operators intertwining first-order and distributed-order derivatives”, Bol. Soc. Mat. Mex., 29:3 (2023)  crossref
    3. B. I. Efendiev, “Zadacha Koshi dlya obyknovennogo differentsialnogo uravneniya vtorogo poryadka s operatorom nepreryvno raspredelennogo differentsirovaniya”, Doklady AMAN, 20:1 (2020), 15–20  mathnet  crossref  elib
    4. B. I. Efendiev, “Zadacha Dirikhle dlya obyknovennogo differentsialnogo uravneniya vtorogo poryadka s operatorom raspredelennogo differentsirovaniya”, Vestnik KRAUNTs. Fiz.-mat. nauki, 29:4 (2019), 48–57  mathnet  crossref
    5. B. I. Efendiev, “Zadacha Neimana dlya obyknovennogo differentsialnogo uravneniya vtorogo poryadka s operatorom raspredelennogo differentsirovaniya”, Izvestiya Kabardino-Balkarskogo nauchnogo tsentra RAN, 2019, no. 5, 30–37  mathnet  crossref  elib
    6. B. I. Efendiev, “The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation”, Math. Notes, 103:2 (2018), 290–296  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. B. I. Efendiev, “Lagrange formula for ordinary continual second-order differential equations”, Differ. Equ., 53:6 (2017), 736–744  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    8. B. I. Efendiev, “Zadacha Koshi i zadacha Dirikhle dlya obyknovennogo differentsialnogo uravneniya vtorogo poryadka s regulyarizovannoi proizvodnoi segmentnogo poryadka”, Izvestiya Kabardino-Balkarskogo nauchnogo tsentra RAN, 2016, no. 2, 30–34  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
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