On the unique solvability of a Cauchy problem with a fractional derivative


Kosmakova M. Akhmetshin A.
March 2023DergiPark

Advances in the Theory of Nonlinear Analysis and its Applications
2023#7Issue 1232 - 242 pp.

The unique solvability issues of the Cauchy problem with a fractional derivative is considered in the case when the coecient 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 sucient conditions for the existence of a solution to the problem are obtained.

Cauchy problem , fractional order dierential equation , kernel singularity , regular solution , Volterra integral equation of the second kind

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Faculty of Mathematics and Information Technologies, Karaganda Buketov University, Karaganda, Kazakhstan

Faculty of Mathematics and Information Technologies

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