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Sbornik: Mathematics, 2011, Volume 202, Issue 4, Pages 571–582
DOI: https://doi.org/10.1070/SM2011v202n04ABEH004156 (Mi sm7645) 		 
This article is cited in 74 scientific papers (total in 74 papers)

Initial-value problem for a linear ordinary differential equation of noninteger order

A. V. Pskhu

Scientific Research Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Centre of the Russian Academy of Sciences
English version PDF (283 kB) Citations (74)
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DOI: https://doi.org/10.1070/SM2011v202n04ABEH004156
Abstract: An initial-value problem for a linear ordinary differential equation of noninteger order with Riemann-Liouville derivatives is stated and solved. The initial conditions of the problem ensure that (by contrast with the Cauchy problem) it is uniquely solvable for an arbitrary set of parameters specifying the orders of the derivatives involved in the equation; these conditions are necessary for the equation under consideration. The problem is reduced to an integral equation; an explicit representation of the solution in terms of the Wright function is constructed. As a consequence of these results, necessary and sufficient conditions for the solvability of the Cauchy problem are obtained.
Bibliography: 7 titles.
Keywords: fractional order derivative, Cauchy problem, differential equation of fractional order, Wright function, Hille-Tamarkin formula.
Received: 29.10.2009
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 4, Pages 111–122
DOI: https://doi.org/10.4213/sm7645
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: 34A99, 26A33
Language: English
Original paper language: Russian
Citation: A. V. Pskhu, “Initial-value problem for a linear ordinary differential equation of noninteger order”, Mat. Sb., 202:4 (2011), 111–122; Sb. Math., 202:4 (2011), 571–582
Citation in format AMSBIB
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    • This publication is cited in the following 74 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:140
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