Geodesic
Finite-Difference Methods for Fractional Differential Equations of Order $1/2$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Functional analysis, Tome 133 (2017), pp. 120-129.

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In this work, we study approximations of solutions of fractional differential equations of order ${1}/{2}$. We present a new method of approximation and obtain the order of convergence. The presentation is given within the abstract framework of a semidiscrete approximation scheme, which includes finite-element methods, finite-difference schemes, and projection methods.
Keywords: fractional Cauchy problem, Banach space, $\alpha$-times resolution family, discretization methods, difference scheme, error estimate. 
@article{INTO_2017_133_a2,
     author = {M. Yu. Kokurin and S. I. Piskarev and M. Spreafico},
     title = {Finite-Difference {Methods} for {Fractional} {Differential} {Equations} of {Order} $1/2$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {120--129},
     publisher = {mathdoc},
     volume = {133},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_133_a2/}
}
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M. Yu. Kokurin; S. I. Piskarev; M. Spreafico. Finite-Difference Methods for Fractional Differential Equations of Order $1/2$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Functional analysis, Tome 133 (2017), pp. 120-129. http://geodesic.mathdoc.fr/item/INTO_2017_133_a2/