On the Operator Method for Solving Linear Integro-Differential Equations with Fractional Conformable Derivatives

Abstract

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.

Keywords

• integro-differential equation
• fractional derivatives
• fractional conformable derivatives
• normalized systems method
• explit solutions
• Mittag–Leffler funtions