Precise Conditions on the Unique Solvability of the Linear Fractional Functional Differential Equations Related to the <i>ς</i>-Nonpositive Operators

Abstract

Exact conditions for the existence of the unique solution of a boundary value problem for linear fractional functional differential equations related to ς-nonpositive operators are established. The exact solvability conditions are based on the a priori estimation method. All theoretical investigations are illustrated by an example of the pantograph-type model from electrodynamics.

Keywords

• fractional order functional differential equations
• nonpositive operator
• unique solvability
• Caputo derivative
• exact conditions
• the pantograph-type model from electrodynamics