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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, Number 8, Pages 79–85 (Mi ivm8921)  
This article is cited in 3 scientific papers (total in 3 papers)

Nonlocal problem with fractional derivatives for mixed type equation

O. A. Repina, S. K. Kumykovab

a Chair of Mathematical Statistics and Econometrics, Samara State Economic University, 141 Sovetskoi Armii str., Samara, 443090 Russia
b Chair of Function Theory, Kabardino-Balkarian State University, 173 Chernyshevskii str., Nalchik, 360004 Russia
Full-text PDF (188 kB) Citations (3)
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Abstract: The paper is devoted to the study of a boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in boundary conditions. Under restrictions inequality type on the known functions and different orders of generalized fractional differentiation operators in boundary conditions we prove the theorem of uniqueness. Existence of the solution is proved by the reductions to equation of Fredholm second sort, which unconditional solvability follows from uniqueness of the solution of the problem.
Keywords: a boundary-value problem, regular solution, operator of fractional integration, operator of fractional differentiation, Fredholm's and Abel's integral equations of the second type, singular integral equation with Cauchy kernel, regularization.
Received: 14.02.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, Volume 58, Issue 8, Pages 65–70
DOI: https://doi.org/10.3103/S1066369X14080088
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: O. A. Repin, S. K. Kumykova, “Nonlocal problem with fractional derivatives for mixed type equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 8, 79–85; Russian Math. (Iz. VUZ), 58:8 (2014), 65–70
Citation in format AMSBIB
\Bibitem{RepKum14}
\by O.~A.~Repin, S.~K.~Kumykova
\paper Nonlocal problem with fractional derivatives for mixed type equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 8
\pages 79--85
\mathnet{http://mi.mathnet.ru/ivm8921}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 8
\pages 65--70
\crossref{https://doi.org/10.3103/S1066369X14080088}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904633597}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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