Theory of Functional Connections Extended to Fractional Operators

Daniele Mortari (), Roberto Garrappa and Luigi Nicolò
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Daniele Mortari: Aerospace Engineering, Texas A&M University, College Station, TX 77845-3141, USA
Roberto Garrappa: Department of Mathematics, Università degli Studi di Bari “Aldo Moro”, 70125 Bari, Italy
Luigi Nicolò: Department of Mathematics, Università degli Studi di Bari “Aldo Moro”, 70125 Bari, Italy

Mathematics, 2023, vol. 11, issue 7, 1-18

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

Keywords: functional interpolation; fractional derivatives and integrals; Riemann–Liouville derivative; shifted Chebyshev polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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