Geodesic
Green's function of a boundary value problem for a system of ordinary differential fractional order equations
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 4, pp. 424-433

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The paper investigates a nonlocal boundary value problem for a linear system of fractional order ordinary differential equations with constant coefficients. The fractional derivative of order $\alpha\in (0,1]$ is understood in the Riemann — Liouville sense. The boundary conditions connect the traces of the fractional integral of the desired vector function at the ends of the segment $[0,l].$ Using the Green's function method, a representation of the solution is obtained, and a theorem on the unique solvability of the boundary value problem under study is proved.
Keywords: system of ordinary differential equations, fractional derivative, nonlocal boundary value problem, Green's function. 
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     author = {M. O. Mamchuev and T. I. Zhabelova},
     title = {Green's function of a boundary value problem for a system of ordinary differential fractional order equations},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
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     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_4_a2/}
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M. O. Mamchuev; T. I. Zhabelova. Green's function of a boundary value problem for a system of ordinary differential fractional order equations. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 4, pp. 424-433. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_4_a2/