Solving of differential equations systems in the presence of fractional derivatives using the orthogonal polynomials

2017;
: pp. 87-95
https://doi.org/10.23939/mmc2017.01.087
Received: July 05, 2017
1
Centre of Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine
2
Centre of Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine
3
Centre of Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine

The mathematical model of the gas motion in the pipelines for the case where unstable process is described by the fractional time derivative is constructed in the paper. The boundary value problem is formulated. The solution of the problem is founded by the spectral method on Chebyshev-Laguerre polynomials bases with respect to the time variable and Legendre polynomials with respect to the coordinate variable. The finding of the solution eventually is reduced to the system of algebraic equations. The numerical experiment is conducted.

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Math. Model. Comput. Vol.4, No.1, pp.87-95 (2017)