03743nam a22005295i 4500 978-3-031-58356-8 DE-He213 20251030112337.0 cr nn 008mamaa 240628s2024 sz | s |||| 0|eng d 9783031583568 978-3-031-58356-8 10.1007/978-3-031-58356-8 doi QA319-329.9 PBKF bicssc MAT037000 bisacsh PBKF thema Rougirel, Arnaud. author. aut http://id.loc.gov/vocabulary/relators/aut 79500 Unified Theory for Fractional and Entire Differential Operators [electronic resource] : An Approach via Differential Quadruplets and Boundary Restriction Operators / by Arnaud Rougirel. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Birkhäuser, 2024. XII, 496 p. 2 illus., 1 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontiers in Elliptic and Parabolic Problems, 2730-5503 Introduction -- 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. This 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. Functional analysis. Operator theory. Differential equations. Functional Analysis. Operator Theory. Differential Equations. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031583551 Printed edition: 9783031583575 Frontiers in Elliptic and Parabolic Problems, 2730-5503 79501 https://doi.org/10.1007/978-3-031-58356-8 ZDB-2-SMA ZDB-2-SXMS 61097 61097