Unique Solvability of the Initial-Value Problem for Fractional Functional Differential Equations—Pantograph-Type Model

Autor:	Natalia Dilna
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	fractional order functional differential equations unique solvability Caputo derivative the model with a discrete memory effect the pantograph-type model from electrodynamics Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 7, Iss 1, p 65 (2023)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract7010065
Popis:	Contrary to the initial-value problem for ordinary differential equations, where the classical theory of establishing the exact unique solvability conditions exists, the situation with the initial-value problem for linear functional differential equations of the fractional order is usually non-trivial. Here we establish the unique solvability conditions for the initial-value problem for linear functional differential equations of the fractional order. The advantage is the lack of the calculation of fractional derivatives, which is a complicated task. The unique solution is represented by the Neumann series. In addition, as examples, the model with a discrete memory effect and a pantograph-type model from electrodynamics are studied.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/442ac0fdb2d94fdb8132535f809ff77a Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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