Geodesic
Fractional diffusion equation with discretely distributed differentiation operator
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1078-1098

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We discuss an initial value problem for a fractional diffusion equation with discretely distributed fractional differentiation operator with respect to time variable. We construct a fundamental solution of the considered equation, give a solution of the problem under study, and prove a uniqueness theorem in the class of rapid growth functions. The fractional differentiation is given by the Dzhrbashyan–Nersesyan operator, and the corresponding results for equations with Caputo and Riemann–Liouville derivatives are particular cases of proved assertions.
Mots-clés : fractional diffusion equation, multi-term fractional diffusion equation
Keywords: Cauchy problem, fractional derivative, discretely distributed fractional differentiation operator, Dzhrbashyan–Nersesyan fractional differentiation operator, Riemann–Liouville derivative, Caputo derivative, Tychonoff condition, Wright function. 
@article{SEMR_2016_13_a86,
     author = {A. V. Pskhu},
     title = {Fractional diffusion equation with discretely distributed differentiation operator},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1078--1098},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a86/}
}
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A. V. Pskhu. Fractional diffusion equation with discretely distributed differentiation operator. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1078-1098. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a86/