Unified Theory for Fractional and Entire Differential Operators
Arnaud Rougirel
Broschiertes Buch

Unified Theory for Fractional and Entire Differential Operators

An Approach via Differential Quadruplets and Boundary Restriction Operators

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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 analy...