03529nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001700188072002300205072001600228100008600244245019300330250001800523264007900541300006300620336002600683337002600709338003600735347002400771490006100795505033400856520141701190650002502607650002102632650002802653650002502681650002102706650002802727710003402755773002602789776003602815776003602851830006802887856004602955912001403001912001503015999001703030978-3-031-58356-8DE-He21320251030112337.0cr nn 008mamaa240628s2024    sz |    s    |||| 0|eng d  a97830315835689978-3-031-58356-87 a10.1007/978-3-031-58356-82doi 4aQA319-329.9 7aPBKF2bicssc 7aMAT0370002bisacsh 7aPBKF2thema1 aRougirel, Arnaud.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97950010aUnified Theory for Fractional and Entire Differential Operatorsh[electronic resource] :bAn Approach via Differential Quadruplets and Boundary Restriction Operators /cby Arnaud Rougirel.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Birkhäuser,c2024.  aXII, 496 p. 2 illus., 1 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aFrontiers in Elliptic and Parabolic Problems,x2730-55030 aIntroduction -- Background on Functional Analysis -- Background on Fractional Calculus -- Differential Triplets on Hilbert Spaces -- Differential Quadruplets on Banach Spaces -- Fractional Differential Triplets and Quadruplets on Lebesgue Spaces -- Endogenous Boundary Value Problems -- Abstract and Fractional Laplace Operators.  aThis monograph proposes a unified theory of the calculus of fractional and standard derivatives by means of an abstract operator-theoretic approach. By highlighting the axiomatic properties shared by standard derivatives, Riemann-Liouville and Caputo derivatives, the author introduces two new classes of objects. The first class concerns differential triplets and differential quadruplets; the second concerns boundary restriction operators. Instances of boundary restriction operators can be generalized fractional differential operators supplemented with homogeneous boundary conditions. The analysis of these operators comprises: The computation of adjoint operators; The definition of abstract boundary values; The solvability of equations supplemented with inhomogeneous abstract linear boundary conditions; The analysis of fractional inhomogeneous Dirichlet Problems. As a result of this approach, two striking consequences are highlighted: Riemann-Liouville and Caputo operators appear to differ only by their boundary conditions; and the boundary values of functions in the domain of fractional operators are closely related to their kernel. Unified Theory for Fractional and Entire Differential Operators will appeal to researchers in analysis and those who work with fractional derivatives. It is mostly self-contained, covering the necessary background in functional analysis and fractional calculus. 0aFunctional analysis. 0aOperator theory. 0aDifferential equations.14aFunctional Analysis.24aOperator Theory.24aDifferential Equations.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303158355108iPrinted edition:z9783031583575 0aFrontiers in Elliptic and Parabolic Problems,x2730-550397950140uhttps://doi.org/10.1007/978-3-031-58356-8  aZDB-2-SMA  aZDB-2-SXMS  c61097d61097