- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 7 Issue: 1
- On the unique solvability of a Cauchy problem with a fractional derivative
On the unique solvability of a Cauchy problem with a fractional derivative
Authors : Minzilya KOSMAKOVA, Aleksandr AKHMETSHİN
Pages : 232-242
Doi:10.31197/atnaa.1216018
View : 115 | Download : 148
Publication Date : 2023-03-31
Article Type : Research Article
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