Abstract:
The unique solvability of internally boundary value problem for equation of mixed type of third order with multiple characteristics is investigated. The uniqueness theorem is proved with the restrictions on certain features and different orders of fractional integro-differentiation. The existence of solution is equivalent reduced to a Fredholm integral equation of the second kind.
Keywords:boundary value problem, fractional integro-differentiation operators, Gauss hypergeometric function, Fredholm integral equation.
Original article submitted 17/X/2011 revision submitted – 23/XI/2011
Citation:
O. A. Repin, S. K. Kumykova, “Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(25) (2011), 25–36
\Bibitem{RepKum11}
\by O.~A.~Repin, S.~K.~Kumykova
\paper Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 4(25)
\pages 25--36
\mathnet{http://mi.mathnet.ru/vsgtu1014}
\crossref{https://doi.org/10.14498/vsgtu1014}
Linking options:
https://www.mathnet.ru/eng/vsgtu1014
https://www.mathnet.ru/eng/vsgtu/v125/p25
This publication is cited in the following 13 articles:
Zh. A. Balkizov, “Nonlocal Boundary-Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with Degeneration of Type and Order in the Hyperbolicity Domain”, J. Math. Sci. (N. Y.), 250:5 (2020), 728–739
Zh. A. Balkizov, “Dirichlet boundary value problem for a third order parabolic-hyperbolic equation with degenerating type and order in the hyperbolicity domain”, Ufa Math. J., 9:2 (2017), 25–39
O. A. Repin, “Zadacha s operatorami Saigo dlya vyrozhdayuschegosya vnutri oblasti giperbolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:3 (2017), 473–480
V. A. Vodakhova, M. R. Yakhutlova, R. G. Tlimakhova, “Nelokalnaya zadacha dlya uravneniya smeshannogo tipa s dvumya perpendikulyarnymi liniyami vyrozhdeniya”, Sovremennye naukoemkie tekhnologii, 2016, no. 2-3, 416–420
O. A. Repin, S. K. Kumykova, “Boundary-value problem with Saigo operators for mixed type equation of the third order with multiple characteristics”, Russian Math. (Iz. VUZ), 59:7 (2015), 44–51
O. A. Repin, S. K. Kumykova, “On a nonlocal problem for a third-order equation of mixed type with multiple characteristics”, Differential Equations, 51:6 (2015), 767–775
Zh. A. Balkizov, “Nelokalnaya kraevaya zadacha dlya modelnogo uravneniya parabolo-giperbolicheskogo tipa tretego poryadka”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 17:4 (2015), 9–20
O. A. Repin, S. K. Kumykova, “Zadacha so smescheniem dlya vyrozhdayuschegosya vnutri oblasti giperbolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(34) (2014), 37–47
Zh. A. Balkizov, “Analog zadachi Trikomi dlya uravneniya parabolo-giperbolicheskogo tipa tretego poryadka s operatorom Gellerstedta v oblasti giperbolichnosti”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 16:2 (2014), 20–27
Zh. A. Balkizov, “Nelokalnaya kraevaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa tretego poryadka s operatorom gellerstedta v oblasti giperbolichnosti”, Uravneniya smeshannogo tipa, rodstvennye problemy analiza i informatiki, Tretii Mezhdunarodnyi Rossiisko-Kazakhskii simpozium, Nalchik, 2014, 47–49
Kh. G. Bzhikhatlov, A. G. Ezaova, “Zadacha s nelokalnymi kraevymi usloviyami dlya uravneniya tretego poryadka”, Izvestiya Kabardino-Balkarskogo gosudarstvennogo universiteta, 3:3 (2013), 26–30
I. G. Mamedov, “Trekhmernaya integro-mnogotochechnaya kraevaya zadacha dlya nagruzhennykh volterro-giperbolicheskikh integro-differentsialnykh uravnenii tipa Bianki”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(26) (2012), 8–20
O. A. Repin, S. K. Kumykova, “Zadacha so smescheniem dlya uravneniya tretego poryadka s razryvnymi koeffitsientami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 4(29) (2012), 17–25