| 书目名称 | Unified Theory for Fractional and Entire Differential Operators |
| 副标题 | An Approach via Diff |
| 编辑 | Arnaud Rougirel |
| 视频video | |
| 概述 | Proposes a unified theory of fractional and entire derivatives.Focuses on the solvability of linear boundary value problems based on usual and fractional differential operators.Establishes the theory |
| 丛书名称 | Frontiers in Mathematics |
| 图书封面 |  |
| 描述 | .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 E |
| 出版日期 | Book 2024 |
| 关键词 | Fractional calculus; Differential quadruplets; Differential triplets; Boundary restriction operators; En |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-58356-8 |
| isbn_softcover | 978-3-031-58355-1 |
| isbn_ebook | 978-3-031-58356-8Series ISSN 1660-8046 Series E-ISSN 1660-8054 |
| issn_series | 1660-8046 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 16:34:22
