Geodesic
Boundary-Value Problems for a Wave Equation of Fractional Order
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 44-55

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A nonlocal wave equation with variable coefficients in a rectangular domain is considered. The first and third boundary-value problems in the differential form are examined; the method of lines in the difference form is applied for solving these problems. For the system of difference equations with constant coefficients arising from the method of lines, a solution is obtained.
Keywords: nonlocal wave equation, fractional derivative, method of lines, a priori estimate. 
@article{INTO_2018_149_a5,
     author = {M. A. Kerefov and B. M. Kerefov},
     title = {Boundary-Value {Problems} for a {Wave} {Equation} of {Fractional} {Order}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {44--55},
     publisher = {mathdoc},
     volume = {149},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_149_a5/}
}
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M. A. Kerefov; B. M. Kerefov. Boundary-Value Problems for a Wave Equation of Fractional Order. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 44-55. http://geodesic.mathdoc.fr/item/INTO_2018_149_a5/