Non-Singular Fractional Kernels as Distributed Relaxation: A Stieltjes Non-Evasion Principle

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Auteur principal: MEGHEZZI, Axel abdel Rahamane
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Publié: Zenodo 2026
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author MEGHEZZI, Axel abdel Rahamane
author_facet MEGHEZZI, Axel abdel Rahamane
contents <p>We study causal Volterra memory operators with non-singular kernels whose Laplace symbols belong to the Stieltjes class. Under these assumptions, the kernel admits a positive representation as a constant zero-relaxation mode, a possible Dirac mass at the origin, and a superposition of exponentially decaying modes. The non-singularity assumption excludes the Dirac contribution, while the absence of a permanent mode yields a finite positive mixture of first-order relaxation channels.</p> <p>This gives a Stieltjes non-evasion principle: within the non-singular Stieltjes class, fractional-looking kernels do not generate autonomous singular fractional dynamics, but reduce structurally to distributed exponential relaxation. The result is applied to the Caputo-Fabrizio, Atangana-Baleanu-Caputo, and Prabhakar-type kernels, clarifying the distinction between being fractional in form and fractional in structure. A brief application to Navier-Stokes equations with memory is also discussed.</p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_19959832
institution Zenodo
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publishDate 2026
publisher Zenodo
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spellingShingle Non-Singular Fractional Kernels as Distributed Relaxation: A Stieltjes Non-Evasion Principle
MEGHEZZI, Axel abdel Rahamane
fractional calculus
non-singular kernels
Stieltjes functions
completely monotone kernels
Volterra memory operators
distributed relaxation
Caputo-Fabrizio kernel
Atangana-Baleanu-Caputo kernel
Mittag-Leffler functions
Prabhakar kernels
Laplace transform
Navier-Stokes equations with memory
<p>We study causal Volterra memory operators with non-singular kernels whose Laplace symbols belong to the Stieltjes class. Under these assumptions, the kernel admits a positive representation as a constant zero-relaxation mode, a possible Dirac mass at the origin, and a superposition of exponentially decaying modes. The non-singularity assumption excludes the Dirac contribution, while the absence of a permanent mode yields a finite positive mixture of first-order relaxation channels.</p> <p>This gives a Stieltjes non-evasion principle: within the non-singular Stieltjes class, fractional-looking kernels do not generate autonomous singular fractional dynamics, but reduce structurally to distributed exponential relaxation. The result is applied to the Caputo-Fabrizio, Atangana-Baleanu-Caputo, and Prabhakar-type kernels, clarifying the distinction between being fractional in form and fractional in structure. A brief application to Navier-Stokes equations with memory is also discussed.</p>
title Non-Singular Fractional Kernels as Distributed Relaxation: A Stieltjes Non-Evasion Principle
topic fractional calculus
non-singular kernels
Stieltjes functions
completely monotone kernels
Volterra memory operators
distributed relaxation
Caputo-Fabrizio kernel
Atangana-Baleanu-Caputo kernel
Mittag-Leffler functions
Prabhakar kernels
Laplace transform
Navier-Stokes equations with memory
url https://doi.org/10.5281/zenodo.19959832