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

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

Kaynakça

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