{"product_id":"9783031583551","title":"Frontiers in Mathematics: An Approach via Differential Quadruplets and Boundary Restriction Operators","description":"\u003ch1\u003eFrontiers in Mathematics: An Approach via Differential Quadruplets and Boundary Restriction Operators\u003c\/h1\u003e \u003ch2\u003eRougirel, Arnaud\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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:\u003c\/p\u003e\n\n\u003cul\u003e\n\t\u003cli\u003eThe computation of adjoint operators;\u003c\/li\u003e\n\t\u003cli\u003eThe definition of abstract boundary values;\u003c\/li\u003e\n\t\u003cli\u003eThe solvability of equations supplemented with inhomogeneous abstract linear boundary conditions;\u003c\/li\u003e\n\t\u003cli\u003eThe analysis of fractional inhomogeneous Dirichlet Problems.\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003cp\u003eAs 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.\u003c\/p\u003e\n\n\u003cp\u003e\u003cem\u003eUnified Theory for Fractional and Entire Differential Operators\u003c\/em\u003e 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2024-06-28\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783031583551\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-031-58356-8\u003c\/p\u003e \u003cp\u003eDimensions: 240cm x168cm\u003c\/p\u003e \u003cp\u003ePages: 496\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45378383478924,"sku":"9783031583551","price":53.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031583551_9b33c0e7-407a-4e0b-b5aa-645e540e748a.jpg?v=1775678481","url":"https:\/\/lateknightbooks.com\/products\/9783031583551","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}