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Unified theory for fractional and entire differential operators = an approach via differential quadruplets and boundary restriction operators /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Unified theory for fractional and entire differential operators/ by Arnaud Rougirel.
Reminder of title:	an approach via differential quadruplets and boundary restriction operators /
Author:	Rougirel, Arnaud.
Published:	Cham :Springer International Publishing : : 2024.,
Description:	xii, 496 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Fractional calculus. -
Online resource:	https://doi.org/10.1007/978-3-031-58356-8
ISBN:	9783031583568

Unified theory for fractional and entire differential operators = an approach via differential quadruplets and boundary restriction operators /
Rougirel, Arnaud.

Unified theory for fractional and entire differential operatorsan approach via differential quadruplets and boundary restriction operators /[electronic resource] :by Arnaud Rougirel. - Cham :Springer International Publishing :2024. - xii, 496 p. :ill. (some col.), digital ;24 cm. - Frontiers in elliptic and parabolic problems,2730-5503. - Frontiers in elliptic and parabolic problems..

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.

ISBN: 9783031583568

Standard No.: 10.1007/978-3-031-58356-8doiSubjects--Topical Terms:

898980
Fractional calculus.

LC Class. No.: QA314

Dewey Class. No.: 515.83

Unified theory for fractional and entire differential operators = an approach via differential quadruplets and boundary restriction operators /
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100 1 $a Rougirel, Arnaud. $3 3719457
245 1 0 $a Unified theory for fractional and entire differential operators $h [electronic resource] : $b an approach via differential quadruplets and boundary restriction operators / $c by Arnaud Rougirel.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2024.
300 $a xii, 496 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Frontiers in elliptic and parabolic problems, $x 2730-5503
505 0 $a 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.
520 $a 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.
650 0 $a Fractional calculus. $3 898980
650 0 $a Differential operators. $3 555718
650 1 4 $a Functional Analysis. $3 893943
650 2 4 $a Operator Theory. $3 897311
650 2 4 $a Differential Equations. $3 907890
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Frontiers in elliptic and parabolic problems. $3 3634535
856 4 0 $u https://doi.org/10.1007/978-3-031-58356-8
950 $a Mathematics and Statistics (SpringerNature-11649)