On a Problem with Conjugation Conditions for an Equation of Even Order Involving a Caputo Fractional Derivative
Matematičeskie zametki, Tome 112 (2022) no. 2, pp. 218-226.

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A problem for an equation of high even order involving a Caputo fractional derivative in a rectangular domain with conjugation conditions is studied. A criterion for the uniqueness of the solution is given. The solution is constructed in the form of a Fourier series in eigenfunctions of a one-dimensional problem.
Keywords: even-order equation, Caputo fractional derivative, discontinuous coefficient, eigenvalue, eigenfunction, Fourier series.
Mots-clés : conjugation conditions
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B. Yu. Irgashev. On a Problem with Conjugation Conditions for an Equation of Even Order Involving a Caputo Fractional Derivative. Matematičeskie zametki, Tome 112 (2022) no. 2, pp. 218-226. http://geodesic.mathdoc.fr/item/MZM_2022_112_2_a5/

[1] A. A. Dezin, “Operatory s pervoi proizvodnoi po “vremeni” i nelokalnye granichnye usloviya”, Izv. AN SSSR. Ser. matem., 31:1 (1967), 61–86 | MR | Zbl

[2] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003 | Zbl

[3] A. N. Bogolyubov, A. A. Koblikov, D. D. Smirnova, N. E. Shapkina, “Matematicheskoe modelirovanie sred s vremennoi dispersiei pri pomoschi drobnogo differentsirovaniya”, Matem. modelirovanie, 25:12 (2013), 50–64 | MR | Zbl

[4] K. B. Sabitov, “Nachalno-granichnaya i obratnye zadachi dlya neodnorodnogo uravneniya smeshannogo parabolo-giperbolicheskogo uravneniya”, Matem. zametki, 102:3 (2017), 415–435 | DOI | MR | Zbl

[5] K. B. Sabitov, “Nelokalnaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa v pryamougolnoi oblasti”, Matem. zametki, 89:4 (2011), 596–602 | DOI | MR | Zbl

[6] K. B. Sabitov, E. M. Safin, “Obratnaya zadacha dlya uravneniya smeshannogo parabolo-giperbolicheskogo tipa”, Matem. zametki, 87:6 (2010), 907–918 | DOI | MR

[7] K. B. Sabitov, “Zadacha Trikomi dlya uravneniya smeshannogo parabolo-giperbolicheskogo v pryamougolnoi oblasti”, Matem. zametki, 86:2 (2009), 273–279 | DOI | MR | Zbl

[8] A. S. Berdyshev, A. Cabada, E. T. Karimov, “On a non-local boundary problem for a parabolic-hyperbolic equation involving a Riemann–Liouville fractional differential operator”, Nonlinear Anal., 75:6 (2012), 3268–3273 | DOI | MR | Zbl

[9] P. Agarwal, A. Berdyshev, E. Karimov, “Solvability of a non-local problem with integral transmitting condition for mixed type equation with Caputo fractional derivative”, Results Math., 71:3 (2017), 1235–1257 | DOI | MR | Zbl

[10] A. S. Berdyshev, E. T. Karimov, N. Akhtaeva, “Boundary value problems with integral gluing conditions for fractional-order mixed-type equation”, Int. J. Differ. Equ., 2011, Art no. 268465 | MR

[11] O. Kh. Abdullaev, K. Sadarangani, “Non-local problems with integral gluing condition for loaded mixed type equations involving the Caputo fractional derivative”, Electron. J. Differential Equations, 2016, Art no. 164 | MR

[12] O. Kh. Masaeva, “Uniqueness of solutions to Dirichlet problems for generalized Lavrent'ev–Bitsadze equations with a fractional derivative”, Electron. J. Differential Equations, 74 (2017), Art no. 74 | MR

[13] P. Feng, E. T. Karimov, “Inverse source problems for time-fractional mixed parabolic-hyperbolic type equations”, J. Inverse Ill-Posed Probl., 23 (2015), 339–353 | DOI | MR | Zbl

[14] R. R. Ashurov, R. T. Zunnunov, “Inverse Problem for Determining the Order of the Fractional Derivative in Mixed-Type Equations”, Lobachevskii J. Math., 42:12 (2021), 2714–2729 | DOI | MR | Zbl

[15] A. S. Berdyshev, A. Cabada, B. J. Kadirkulov, “The Samarskii–Ionkin type problem for the fourth order parabolic equation with fractional differential operator”, Comput. Math. Appl., 62 (2011), 3884–3893 | DOI | MR | Zbl

[16] A. S. Berdyshev, J. B. Kadirkulov, “On a nonlocal problem for a fourth-order parabolic equation with the fractional Dzhrbashyan–Nersesyan operator”, Differ. Equ., 52:1 (2016), 122–127 | DOI | MR | Zbl

[17] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud., 204, Elsevier, Amsterdam, 2006 | MR | Zbl

[18] M. A. Naimark, Lineinye differentsialnye operatory, Nauka, M., 1969 | MR | Zbl

[19] M. M. Dzhrbashyan, Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966 | MR | Zbl

[20] A. V. Pskhu, “O veschestvennykh nulyakh funktsii tipa Mittag-Lefflera”, Matem. zametki, 77:4 (2005), 592–599 | DOI | MR | Zbl

[21] A. V. Pskhu, Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005 | MR | Zbl

[22] H. Pollard, “The completely monotonic character of the Mittag-Leffler function $E_a({-x})$”, Bull. Amer. Math. Soc., 54 (1948), 1115–1116 | DOI | MR | Zbl

[23] JinRong Wang, Yong Zhou, D. O'Regan, “A note on asymptotic behaviour of Mittag-Leffler functions”, Integral Transforms Spec. Funct., 29:2 (2018), 81–94 | DOI | MR | Zbl