On the unique solvability of a Cauchy problem with a fractional derivative - Kosmakova, M.; Akhmetshin, A. (Advances in the Theory of Nonlinear Analysis and its Applications 7 (2023) No. 1, 232 242., 2023)
The unique solvability issues of the Cauchy problem with a fractional derivative is considered in the case when the coe cient at the desired function is a continuous function. The solution of the problem is found in an explicit form. The uniqueness theorem is proved. The existence theorem for a solution to the problem is proved by reducing it to a Volterra equation of the second kind with a singularity in the kernel, and the necessary and su cient conditions for the existence of a solution to the problem are obtained.