Geodesic
Probabilistic representation for Cauchy problem solution for evolution equation with Riemann--Liouville operator
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 417-438

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This paper studies properties of probabilistic approximation of a solution of the Cauchy problem for evolution equations with fractional differential operators of order more than two. To this end we construct analogous one-sided $\alpha$-stable distributions for noninteger $\alpha>2$. Although densities of these distributions are signed functions, using generalized functions methods, it is possible to give them an exact probability sense.
Keywords: Liouville–Riemann operator
Mots-clés : evolution equation, stable distribution. 
@article{TVP_2016_61_3_a0,
     author = {M. V. Platonova},
     title = {Probabilistic representation for {Cauchy} problem solution for evolution equation with {Riemann--Liouville} operator},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {417--438},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a0/}
}
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M. V. Platonova. Probabilistic representation for Cauchy problem solution for evolution equation with Riemann--Liouville operator. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 417-438. http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a0/