Fractional Scale Calculus: Hadamard vs. Liouville-Reference-Cited by-同舟云学术

Fractional Scale Calculus: Hadamard vs. Liouville

Published:2023-03-29 Issue:4 Volume:7 Page:296
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Ortigueira Manuel D.¹^ORCID,Bohannan Gary W.²^ORCID

Affiliation:

1. Centre of Technology and Systems–UNINOVA and Department of Electrical Engineering, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal

2. 9248 Liggon Green Lane, Germantown, TN 38139, USA

Abstract

A general fractional scale derivative is introduced and studied. Its relation with the Hadamard derivatives is established and reformulated. A new derivative similar to the Grünwald–Letnikov’s is deduced. Tempered versions are also introduced. Scale-invariant systems are described and exemplified. For solving the corresponding differential equations, a new logarithmic Mittag-Leffler series is proposed.

Funder

Foundation for Science and Technology of Portugal

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/4/296/pdf

Reference66 articles.

1. The scale representation;Cohen;IEEE Trans. Signal Process.,1993

2. The theory of scale relativity;Nottale;Int. J. Mod. Phys. A,1992

3. Nottale, L. (2001, January 24–29). Non-differentiable space-time and scale relativity. Proceedings of the International Colloquium Geometrie au XXe Siecle, Paris, France.

4. The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time;Dubois;Computing Anticipatory Systems. CASYS’03—Sixth International Conference. American Institute of Physics Conference Proceedings,2004

5. Scale relativity theory for one-dimensional non-differentiable manifolds;Cresson;Chaos Solitons Fractals,2002

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