Darboux problem for a differential equation with fractional derivative |
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Authors: | A N Vityuk A V Golushkov |
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Institution: | (1) Institute of Mathematics, Economics, and Mechanics, Mechnikov Odessa National University, Odessa |
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Abstract: | We find conditions for the unique solvability of the problem u
xy
(x, y) = f(x, y, u(x, y), (D
0
r
u)(x, y)), u(x, 0) = u(0, y) = 0, x ∈ 0, a], y ∈ 0, b], where (D
0
r
u)(x, y) is the mixed Riemann-Liouville derivative of order r = (r
1, r
2), 0 < r
1, r
2 < 1, in the class of functions that have the continuous derivatives u
xy
(x, y) and (D
0
r
u)(x, y). We propose a numerical method for solving this problem and prove the convergence of the method.
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Translated from Neliniini Kolyvannya, Vol. 8, No. 4, pp. 456–467, October–December, 2005. |
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Keywords: | |
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