{"product_id":"unified-theory-for-fractional-and-entire-differential-operators-von-arnaud-rougirel","title":"Unified Theory for Fractional and Entire Differential Operators","description":"\n                                \n                \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                \n                \u003cul\u003e\n                                        \t\n                    \n                    \u003cli\u003eThe computation of adjoint operators;\u003c\/li\u003e\n                                        \t\n                    \n                    \u003cli\u003eThe definition of abstract boundary values;\u003c\/li\u003e\n                                        \t\n                    \n                    \u003cli\u003eThe solvability of equations supplemented with inhomogeneous abstract linear boundary conditions;\u003c\/li\u003e\n                                        \t\n                    \n                    \u003cli\u003eThe analysis of fractional inhomogeneous Dirichlet Problems.\u003c\/li\u003e\n                                        \n                \n                \u003c\/ul\u003e\n                                \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                \n                \u003cp\u003e\n                                        \n                    \u003cem\u003eUnified Theory for Fractional and Entire Differential Operators\u003c\/em\u003e\n                                         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.\n                \n                \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031583551\"\u003e\u003ch3\u003eAn Approach via Differential Quadruplets and Boundary Restriction Operators\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783031583551","offer_id":49677897367877,"sku":"9783031583551","price":58.84,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/7404615e-7fbb-4030-ae46-e63c8c0ef9a6.jpg?v=1772169944","url":"https:\/\/shop.autorenwelt.de\/products\/unified-theory-for-fractional-and-entire-differential-operators-von-arnaud-rougirel","provider":"Autorenwelt Shop","version":"1.0","type":"link"}