Geodesic
Dirichlet Problem for Second-Order Ordinary Differential Equations with Segment-Order Derivative
Matematičeskie zametki, Tome 97 (2015) no. 4, pp. 620-628.

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The fundamental solution of a second-order ordinary differential equation with segment-order derivative is constructed. The Green function of the Dirichlet problem is determined on the basis the fundamental solution and the solution of the Dirichlet problem for the equation under study is obtained under the solvability condition.
Keywords: second-order ordinary differential equation, Dirichlet problem, segment-order derivative, Green function, fundamental solution, Euler gamma function. 
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B. I. Efendiev. Dirichlet Problem for Second-Order Ordinary Differential Equations with Segment-Order Derivative. Matematičeskie zametki, Tome 97 (2015) no. 4, pp. 620-628. http://geodesic.mathdoc.fr/item/MZM_2015_97_4_a11/

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