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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 3, Pages 22–30 (Mi vmj586)  

This article is cited in 6 scientific papers (total in 6 papers)

Neumann problem for an ordinary differential equation of fractional order

L. H. Gadzova

Institute of Applied Mathematics and Automation, Nalchik, Russia

Abstract: A linear ordinary differential equation of fractional order with constant coefficients is considered in the paper. Such equation should be subsumed into the class of discretely distributed order, or multi-term differential equations. The fractional differentiation is given by the Caputo derivative. We solve The Nuemann problem for the equation under study, prove the existence and uniqueness of the solution, find an explicit representation for solution in terms of the Wright function, and construct the respective Green function. It is also prove that the real part of the spectrum of the problem may consist at most of a finite number of eigenvalues.

Key words: boundary value problem, operator of fractional differentiation, Riemann–Liouville operator, Caputo operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00462


Full text: PDF file (217 kB)
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UDC: 517.91
Received: 01.04.2015

Citation: L. H. Gadzova, “Neumann problem for an ordinary differential equation of fractional order”, Vladikavkaz. Mat. Zh., 18:3 (2016), 22–30

Citation in format AMSBIB
\Bibitem{Gad16}
\by L.~H.~Gadzova
\paper Neumann problem for an ordinary differential equation of fractional order
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 3
\pages 22--30
\mathnet{http://mi.mathnet.ru/vmj586}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. Kh. Gadzova, “Nelokalnaya kraevaya zadacha dlya obyknovennogo differentsialnogo uravneniya s operatorom diskretno raspredelennogo differentsirovaniya”, Izvestiya Kabardino-Balkarskogo nauchnogo tsentra RAN, 2017, no. 1, 12–18  mathnet
    2. L. Kh. Gadzova, “Zadacha Koshi dlya obyknovennogo differentsialnogo uravneniya s operatorom drobnogo diskretno raspredelennogo differentsirovaniya”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 3(23), 48–56  mathnet  crossref  elib
    3. L. Kh. Gadzova, “Boundary value problem for a linear ordinary differential equation with a fractional discretely distributed differentiation operator”, Differ. Equ., 54:2 (2018), 178–184  crossref  mathscinet  zmath  isi  scopus
    4. L. Kh. Gadzova, “Kraevaya zadacha so smescheniem dlya lineinogo obyknovennogo differentsialnogo uravneniya s operatorom diskretno raspredelennogo differentsirovaniya”, Materialy mezhdunarodnoi nauchnoi konferentsii Aktualnye problemy prikladnoi matematiki i fiziki Kabardino-Balkariya, Nalchik, 1721 maya 2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 149, VINITI RAN, M., 2018, 25–30  mathnet  mathscinet
    5. L. Kh. Gadzova, “Nonlocal Boundary-Value Problem for a Linear Ordinary Differential Equation with Fractional Discretely Distributed Differentiation Operator”, Math. Notes, 106:6 (2019), 904–908  mathnet  crossref  crossref  mathscinet  isi  elib
    6. L. Kh. Gadzova, “Funktsiya Grina vnutrennei kraevoi zadachi dlya obyknovennogo differentsialnogo uravneniya drobnogo poryadka s postoyannymi koeffitsientami”, Materialy mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu v prikladnykh naukakh “International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19”. Belgorod, 20–24 avgusta 2019 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 195, VINITI RAN, M., 2021, 25–34  mathnet  crossref
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