ARTICLE | doi:10.20944/preprints202108.0055.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: integro-differential equation; fractional derivatives; fractional conformable derivatives; normalized systems method.
Online: 2 August 2021 (15:46:38 CEST)
The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.