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

Year 2023, Volume: 7 Issue: 1, 232 - 242, 31.03.2023

Minzilya Kosmakova , Aleksandr Akhmetshin

https://doi.org/10.31197/atnaa.1216018

Abstract

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

Keywords

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

Thanks

This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09259780, 2021-2023.)

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