Дослiджено лiнiйну крайову задачу для багаточленного диференцiального рiвняння
дробового порядку з похiдною Капуто. У випадку спiвмiрних порядкiв похiдної, використовуючи апарат теорiї псевдообернених матриць, встановлено необхiднi та достатнi умови
розв’язностi та знайдено загальний вигляд розв’язку поставленої задачi.

[1] Atanackovi´c T.M., Pilipovi´c S., Stankovi´c B., Zorica D. Fractional calculus with applications
in mechanics: vibrations and diffusion processes. Wiley-ISTE, London; Hoboken, 2014.
doi:10.1002/9781118577530
[2] Boichuk O.A., Feruk V.A. Fredholm boundary-value problem for the system of fractional differential
equations. Nonlinear Dyn. 2023, 111, 7459–7468. doi:10.1007/s11071-022-08218-4
[3] Boichuk A.A., Samoilenko A.M. Generalized inverse operators and Fredholm boundary-value problems
(2th ed.). De Gruyter, Berlin; Boston, 2016. doi:10.1515/9783110378443
[4] Caputo M. Lineal model of dissipation whose Q is almost frequency independent - II. Geophys. J. R.
Astr. Soc. 1967, 13 (5), 529–539. doi:10.1111/j.1365-246X.1967.tb02303.x
[5] Dabiri A., Butcher E.A. Stable fractional Chebyshev differentiation matrix for the numerical solution
of multi-order fractional differential equations. Nonlinear Dyn. 2017, 90, 185–201. doi:10.1007/s11071-
017-3654-3
[6] Deng W., Li C., Guo Q. Analysis of fractional differential equations with multi-orders. Fractals. 2007,
15 (2), 173–182. doi:10.1142/S0218348X07003472
[7] Diethelm K. The analysis of fractional differential equations: an application-oriented exposition using
differential operators of Caputo type. Springer, Berlin; Heidelberg, 2010. doi:10.1007/978-3-642-14574-2
[8] Diethelm K., Ford N.J. Multi-order fractional differential equations and their numerical solution. Appl.
Math. Comput. 2004, 154 (3), 621–640. doi:10.1016/S0096-3003(03)00739-2
[9] Dzherbashyan M.M., Nersesyan A.B. Fractional derivatives and the Cauchy problem for differential
equations of fractional order. Izv. Akad. Nauk Armyan. SSR, Ser. Mat. 1968, 3 (1), 3–29. (in Russian)
[10] Erturk V.S., Momani S., Odibat Z. Application of generalized differential transform method to multiorder
fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 2008, 13 (8), 1642–1654.
doi:10.1016/j.cnsns.2007.02.006
[11] Gerasimov A.N. Generalization of laws of the linear deformation and their application to problems of
the internal friction. Prikl. Mat. Meh. 1948, 12 (3), 251–260. (in Russian)
[12] Goursat E. A course in mathematical analysis, Vol. III, Part. 2. Dover Publications, Inc., New York,
1964.
[13] Kochubei A.N. General fractional calculus, evolution equations, and renewal processes. Integral Equ.
Oper. Theory. 2011, 71 (4), 583–600. doi:10.1007/s00020-011-1918-8
[14] Liouville J. Memoire sur quelques questions de geometrie et de mecanique, et sur un nouveau gentre
pour resoudre ces quistions. J. Ecole Polytech. 1832, 13, 1–69.
[15] Podlubny I. Fractional differential equations, Mathematics in science and engineering. Academic Press,
San Diego, 1999.
[16] Shloof A.M., Ahmadian A., Senu N., Salahshour S., Ibrahim S.N.I., Pakdaman M. A highly accurate
artificial neural networks scheme for solving higher multi-order fractal-fractional differential equations
based on generalized Caputo derivative. Int. J. Numer. Methods Eng. 2023, 124 (19), 4371–4404.
doi:10.1002/nme.7312
[17] Weyl H. Bemerkungen zum begriff des differentialquotienten gebrochener ordnung. Z¨urich. Naturf. Ges.
1917, 62, 296–302.