Evolution Equations with Liouville Derivative on R without Initial Conditions

Autor:	Vladimir E. Fedorov, Nadezhda M. Skripka
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Liouville derivative differential equation without initial conditions Fourier transform Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 4, p 572 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12040572
Popis:	New classes of evolution differential equations with the Liouville derivative in Banach spaces are studied. Equations are considered on the whole real line and are not endowed by the initial conditions. Using the methods of the Fourier transform theory, we prove the unique solvability in the sense of classical solutions for the equation solved with respect to the Liouville fractional derivative with a bounded operator at the unknown function. This allows us to obtain the analogous result for the equation with a linear degenerate operator at the fractional derivative and with a spectrally bounded pair of operators. Abstract results are applied to obtain new results on the unique solvability of systems of ordinary differential equations, boundary problems to partial differential equations, and systems of equations.
Databáze:	Directory of Open Access Journals
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