Geodesic
To boundary-value problems for degenerating pseudoparabolic equations with Gerasimov--Caputo fractional derivative
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2018), pp. 3-16

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In this paper we consider a boundary-value problems for degenerating pseudoparabolic equation with variable coefficients and with Gerasimov–Caputo fractional derivative. To solve the problem we obtain apriori estimates in differential and difference settings. These apriori estimates imply uniqueness and stability of the solution with respect to the initial data and the right-hand side on the layer, as well as the convergence of the solution of each of the difference problem to the solution of the corresponding differential problem.
Keywords: boundary-value problem, apriori estimate, difference scheme, the equation of pseudoparabolic type, differential equation of fractional order, Gerasimov–Caputo fractional derivative. 
@article{IVM_2018_10_a0,
     author = {M. Kh. Beshtokov},
     title = {To boundary-value problems for degenerating pseudoparabolic equations with {Gerasimov--Caputo} fractional derivative},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--16},
     publisher = {mathdoc},
     number = {10},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_10_a0/}
}
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M. Kh. Beshtokov. To boundary-value problems for degenerating pseudoparabolic equations with Gerasimov--Caputo fractional derivative. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2018), pp. 3-16. http://geodesic.mathdoc.fr/item/IVM_2018_10_a0/