Representation of Fractional Operators Using the Theory of Functional Connections

Daniele Mortari ()
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Daniele Mortari: Aerospace Engineering, Texas A&M University, College Station, TX 77845-3141, USA

Mathematics, 2023, vol. 11, issue 23, 1-16

Abstract: This work considers fractional operators (derivatives and integrals) as surfaces f ( x , α ) subject to the function constraints defined by integer operators, which is a mandatory requirement of any fractional operator definition. In this respect, the problem can be seen as the problem of generating a surface constrained at some positive integer values of α for fractional derivatives and at some negative integer values for fractional integrals. This paper shows that by using the Theory of Functional Connections, all (past, present, and future) fractional operators can be approximated at a high level of accuracy by smooth surfaces and with no continuity issues. This practical approach provides a simple and unified tool to simulate nonlocal fractional operators that are usually defined by infinite series and/or complicated integrals.

Keywords: functional interpolation; fractional derivative; fractional integral; Mittag–Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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