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Unified Theory for Fractional and Entire Differential Operators: An Approach via Differential Quadruplets and Boundary Restriction Operators (Frontiers in Mathematics)
3031583558 pdf 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 Read more