The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
Generalized viscoelastic models: their fractional equations with solutions
Open accessAbstract
Recently fractional calculus (FC) has encountered much success in the description of complex dynamics. In particular FC has proved to be a valuable tool to handle viscoelastic aspects. In this paper we construct fractional rheological constitutive equations on the basis of well known mechanical models, especially the Maxwell, the Kelvin-Voigt, the Zener and the Poynting-Thomson model. To this end we introduce a fractional element, in addition to the standard purely elastic and purely viscous elements. As we proceed to show, many of the fractional differential equations which we obtain by this construction method admit closed form, analytical solutions in terms of Fox H-functions of the Minag-Leffler type.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
Cole, K. S., & Cole, R. H. (1941) · The Journal of Chemical Physics · doi:10.1063/1.1750906 · Cited by 10,152
The theory of polymer dynamics
Doi, M., & Edwards, S. F. (1986) · Cited by 8,928
An Introduction to the Fractional Calculus and Fractional Differential Equations
Miller, K. S., & Ross, B. (1993) · Cited by 8,193
The ‘universal’ dielectric response
Jonscher, A. K. (1977) · Nature · doi:10.1038/267673a0 · Cited by 5,618
Anomalous transit-time dispersion in amorphous solids
Scher, H., & Montroll, E. W. (1975) · Physical Review B · doi:10.1103/physrevb.12.2455 · Cited by 3,107
Mechanical Properties of Solid Polymers: Third Edition
Ward, I. M., & Sweeney, J. (2012) · Wiley eBooks · doi:10.1002/9781119967125 · Cited by 2,084
The Phenomenological Theory of Linear Viscoelastic Behavior
Tschoegl, N. W. (1989) · Springer eBooks · doi:10.1007/978-3-642-73602-5 · Cited by 1,328
Linear Viscoelasticity at the Gel Point of a Crosslinking PDMS with Imbalanced Stoichiometry
Chambon, F., & Winter, H. H. (1987) · Journal of Rheology · doi:10.1122/1.549955 · Cited by 1,246
Thermodynamics of irreversible processes
GROOT, S. R. D. (1951) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,197
Relaxation in filled polymers: A fractional calculus approach
Metzler, R., Schick, W., Kilian, H.-G., & Nonnenmacher, T. F. (1995) · The Journal of Chemical Physics · doi:10.1063/1.470346 · Cited by 516
Self-citation
Cited by
Jaishankar, A., & McKinley, G. H. (2013) · Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2012.0284 · Cited by 332
Sinkus, R., Siegmann, K., Xydeas, T., Tanter, M., Claussen, C., & Fink, M. (2007) · Magnetic Resonance in Medicine · doi:10.1002/mrm.21404 · Cited by 332
Metadata
- Authors
- Schiessel, H., Metzler, R., Blumen, A., & Nonnenmacher, T. F.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1995-12-07
- Volume
- 28
- Issue
- 23
- Pages
- 6567-6584
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2015260916
- Cited by
- 629
- References
- 16
- FWCI
- 5.44
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Generalized viscoelastic models: their fractional equations with solutions. https://app.cochat.ai/papers/10.1088/0305-4470/28/23/012
- The paper
- Schiessel, H., Metzler, R., Blumen, A., & Nonnenmacher, T. F. (1995). Generalized viscoelastic models: their fractional equations with solutions. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/28/23/012
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
