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Unified Theory for Fractional and Entire Differential Operators : An Approach Via Differential Quadruplets and Boundary Restriction Operators by Springer International Publishing AG, University of Poitiers is a nonfiction available to read on EtoBox.
What is Unified Theory for Fractional and Entire Differential Operators : An Approach Via Differential Quadruplets and Boundary Restriction Operators about?
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
Who reads Unified Theory for Fractional and Entire Differential Operators : An Approach Via Differential Quadruplets and Boundary Restriction Operators?
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Common subject areas: history, science, philosophy, social sciences.
- Author
- Springer International Publishing AG, University of Poitiers
- Publisher
- Birkhäuser
- Published
- 2024
- Language
- EN
- ISBN
- 9783031583568
- Category
- nonfiction
- Subjects
- Mathematics, Stem
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