On a method for constructing a solution of integro-differential equations of fractional order

Abstract

In this paper, we propose a new method for constructing a solution of the integro-differential equations of Volterra type. The particular solutions of the homogeneous and of the inhomogeneous equation will be constructed and the Cauchy type problems will be investigated. Note that this method is based on construction of normalized systems functions with respect to the differential operator's fractional order.

Keywords

• integro-differential equation of volterra type
• riemann–liouville fractional integrals and derivatives
• generalized mittag-leffler function
• method normalized systems of functions