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.
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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/

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