Unified Theory

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:

Concern about psychology’s fragmentation is not new, but there has for the past decade been increasing calls for psychologists to acknowledge to the costs associated with fragmentation and to search for ways to unify the discipline.

This volume develops an integrated theory that encompasses the various stress states experienced by both RC & PC structures under the various loading conditions of bending, axial load, shear and torsion. Upon synthesis, the new rational theories replace the many empirical formulas currently in use for shear, torsion and membrane stress.