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

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Advances in the Theory of Nonlinear Analysis and its Application
Volume: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 : 123 | Download : 159

Publication Date : 2023-03-31

Article Type : Research Paper

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

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