Localized derivatives in spaces of functions representable by localized fractional integrals

The form of a localized fractional derivative of the Marchaud type is obtained. The compositions of localized fractional Riemann-Liouville and Marchaud type derivatives and localized fractional integrals are considered. For homogeneous differential equations with such compositions, non-local uniquen...

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Bibliographic Details
Published in:Integral transforms and special functions 2019-10, Vol.30 (10), p.817-832
Main Author: Grinko, A. P.
Format: Article
Language:English
Subjects:
Composition
composition localized fractional derivatives and integrals
Derivatives
Differential equations
differential equations with localized fractional derivatives
Fractional derivatives and integrals
Initial conditions
initial value problems for differential equations with localized fractional derivatives
Integrals
local fractional derivatives and integrals
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Summary:The form of a localized fractional derivative of the Marchaud type is obtained. The compositions of localized fractional Riemann-Liouville and Marchaud type derivatives and localized fractional integrals are considered. For homogeneous differential equations with such compositions, non-local uniqueness conditions for the solution are obtained. A physical interpretation of such initial conditions is given.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2019.1623794