Year: 2024
Type: article
Abstract: The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials Cn(ν)(x), where ν>−12. Building on the work of Diekema and Koornwinder, the n-th derivative is obtained as the limit of an integral involving Gegenbauer polynomials as the kernel. When this limit is omitted, it results in the approximate Gegenbauer orthogonal derivative, which serves as an effective approximation of the n-th order derivative. Using this operator, we introduce a novel extension of the fractional Riesz derivative, denoted as Dαx, providing an alternative framework for fractional calculus.
Source: Axioms
Author: Fethi Bouzeffour
Institution: King Saud University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
Funder: King Saud University
Award: G4827175253
OpenAlex ID: W4403453643