Geodesic
A finite difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 38-51

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We study a well-posed Cauchy problem with a fractional Caputo derivative of the order $\alpha\in(0,1)$ in a Banach space. We build and explore a finite difference scheme on a graded mesh for solving such problems. The stability and accuracy estimates for a proposed finite difference scheme are obtained.
Keywords: Cauchy problem, Caputo derivative, Banach space, finite difference scheme, stability, accuracy estimate, graded mesh, full discretization. 
@article{IVM_2022_11_a3,
     author = {M. M. Kokurin and S. I. Piskarev},
     title = {A finite difference scheme on a graded mesh for solving {Cauchy} problems with a fractional {Caputo} derivative in a {Banach} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {38--51},
     publisher = {mathdoc},
     number = {11},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_11_a3/}
}
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M. M. Kokurin; S. I. Piskarev. A finite difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 38-51. http://geodesic.mathdoc.fr/item/IVM_2022_11_a3/