General exact solvability conditions for the initial value problems for linear fractional functional differential equations

Natalia Dilna

Address: Institute of Mathematics, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia

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Abstract: Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.

AMSclassification: primary 26A33; secondary 34A08, 34B15.

Keywords: fractional order functional differential equations, Caputo derivative, normal and reproducing cone, unique solvability.

DOI: 10.5817/AM2023-1-11