On the solution of the Cauchy problem for a higher-order equation with the fractional Riemann-Liouville derivative

Research Article

On the solution of the Cauchy problem for a higher-order equation with the fractional Riemann-Liouville derivative

Published in: Quaestiones Mathematicae
Volume 47 , issue 7 , 2024 , pages: 1339–1352
DOI: 10.2989/16073606.2024.2320444
Author(s): B.Yu. Irgashev New Uzbekistan University, Uzbekistan
Keywords: 35G10 , 35C06 , 33N20 , Higher order equation , fractional Riemann-Liouville derivative , Wright function , Cauchy problem , solution representation
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Abstract

In this article, a representation of the solution of the Cauchy problem for an equation of high even order with a fractional derivative in the Riemann-Liouville sense of order greater than one is obtained. The uniqueness of the solution is proved.
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