Theory of Functional Connections Extended to Fractional Operators

The theory of functional connections, an analytical framework generalizing interpolation, was extended and applied in the context fractional-order operators (integrals derivatives). extension performed presented for univariate functions, with aim determining whole set functions satisfying some constraints expressed terms integrals derivatives non-integer order. objective these expressions to solve fractional differential equations or other problems subject constraints. Although this work focused on Riemann–Liouville definitions, method is, however, more general, it can be different definitions just by changing way they are computed. Three examples provided showing, step step, how apply for: (1) one constraint a derivative, (2) three (a function, integral), (3) two linear combinations integrals.