Geodesic
Оn а рrоblеm fоr thе lоаdеd miхеd tуре еquаtiоn with frасtiоnаl dеrivаtivе
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2016), pp. 7-14
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An existence and an uniqueness of solution of local boundary value problem with discontinuous matching condition for the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals have been investigated in this research work. The uniqueness of solution is proved by the method of integral energy and the existence is proved by the method of integral equations.
Keywords: Caputo derivative, boundary value problem, Riemann-Liouville integral, energy integral. 
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     author = {O. Kh. Abdullaev},
     title = {{\CYRO}n {\cyra} {\cyrr}r{\cyro}bl{\cyre}m f{\cyro}r th{\cyre} l{\cyro}{\cyra}d{\cyre}d mi{\cyrh}{\cyre}d t{\cyru}{\cyrr}{\cyre} {\cyre}qu{\cyra}ti{\cyro}n with fr{\cyra}{\cyrs}ti{\cyro}n{\cyra}l d{\cyre}riv{\cyra}tiv{\cyre}},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {7--14},
     year = {2016},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2016_1_a0/}
}
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O. Kh. Abdullaev. Оn а рrоblеm fоr thе lоаdеd miхеd tуре еquаtiоn with frасtiоnаl dеrivаtivе. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2016), pp. 7-14. http://geodesic.mathdoc.fr/item/VKAM_2016_1_a0/

[1] Kadirkulov B. J., “Boundary problems for mixed parabolic-hyperbolic equations with two lines of changing type and fractional derivative”, Electronic Journal of Differential Equations, 2014:57 (2014), 1–7 | MR

[2] Karimov E. T., Akhatov J., “A boundary problem with integral gluing condition for a parabolic-hyperbolic equation involving the Caputo fractional derivative”, Electronic Journal of Differential Equations, 2014:14 (2014), 1–6 | MR

[3] Nakhushev A. M., Nagruzhennye uravneniya i ikh prilozheniya, Nauka, M., 2012, 232 pp.

[4] Eleev V. A., “O nekotorykh kraevykh zadachakh dlya smeshanno-nagruzhennykh uravneniy vtorogo i tret'ego poryadka”, Differentsial'nye uravneniya, 30:2 (1994), 230–236 | MR

[5] Kaziev V. M., “O zadache Darbu dlya odnogo nagruzhennogo integro-differentsial'nogo uravneniya vtorogo poryadka”, Differentsial'nye uravneniya, 14:1 (1978), 181–184 | MR | Zbl

[6] Lanin I. N., “Kraevaya zadacha dlya odnogo nagruzhennogo giperbolo-parabolicheskogo uravneniya tret'ego poryadka”, Differentsial'nye uravneniya, 17:1 (1981), 97–106 | MR | Zbl

[7] Abdullaev O. Kh., “Kraevaya zadacha dlya nagruzhennogo uravneniya elliptiko-giperbolicheskogo tipa v dvusvyaznoy oblasti”, Vestnik KRAUNTS. Fiz.-mat. nauki, 2014, no. 1(8), 33–48

[8] Abdullaev O. Kh., “About a method of research of the non-local problem for the loaded mixed type equation in double-connected domain”, Bulletin KRASEC. Phys. Math. Sci., 2014, no. 9(2), 11–16

[9] Abdullaev O. Kh., “Non-local boundary value problem for the mixed type equations on the third order in double-connected domains”, Journal of Partial Differential Equations, 27:4 (2014), 283–292 | MR

[10] “Nelokal'naya zadacha dlya nagruzhennogo uravneniya smeshannogo tipa s integral'nym operatorom”, Differentsial'nye uravneniya i matematicheskoe modelirovanie, Mezhdunarodnaya konferentsiya (Ulan-Ude, 2015), VSGUTU, Ulan-Ude, 2015, 21-23

[11] Pskhu A. V., Uravneniye v chasnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005, 200 pp. | MR

[12] Smirnov M. M., Uravneniya smeshannogo tipa, Nauka, M., 1970, 296 pp. | MR

[13] Pskhu A. V., “Solution of boundary value problems fractional diffusion equation by the Green function method”, Differential equation, 39:10 (2003), 1509–1513 | DOI | MR | Zbl