Non-Singular Fractional Kernels as Distributed Relaxation: A Stieltjes Non-Evasion Principle
Fuente:
Zenodo
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Publié: |
Zenodo
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866901236871069696 |
|---|---|
| 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 |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| 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 |