The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
Abstract
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag–Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined.
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
A new collection of real world applications of fractional calculus in science and engineering
Sun, H., Zhang, Y., Baleanu, D., Chen, W., & Chen, Y. (2018) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2018.04.019 · Cited by 1,777
Self-citationNonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis
Kuznetsov, V. A., Makalkin, I. A., Taylor, M. A., & Perelson, A. S. (1994) · Bulletin of Mathematical Biology · doi:10.1007/bf02460644 · Cited by 1,061
The role of fractional calculus in modeling biological phenomena: A review
Ionescu, C., Lopes, A., Copot, D., Machado, J. A. T., & Bates, J. H. T. (2017) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2017.04.001 · Cited by 729
A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth
de Pillis, L. G., Radunskaya, A. E., & Wiseman, C. L. (2005) · Cancer Research · doi:10.1158/0008-5472.can-05-0564 · Cited by 649
de Pillis, L. G., Gu, W., & Radunskaya, A. E. (2006) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2005.06.037 · Cited by 575
Vasas, V., Fernando, C., Santos, M., Kauffman, S., & Szathmáry, E. (2012) · Biology Direct · doi:10.1186/1745-6150-7-1 · Cited by 369
de Pillis, L. G., Gu, W., Fister, K. R., Head, T., Maples, K., Murugan, A., Neal, T., & Yoshida, K. (2007) · Mathematical Biosciences · doi:10.1016/j.mbs.2006.05.003 · Cited by 245
An evolutionary hybrid cellular automaton model of solid tumour growth
Gerlee, P., & Anderson, A. R. A. (2007) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2007.01.027 · Cited by 220
Fractional modeling of blood ethanol concentration system with real data application
Qureshi, S., Yusuf, A., Shaikh, A. A., Inc, M., & Baleanu, D. (2019) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5082907 · Cited by 199
Self-citationReinforcement learning-based control of drug dosing for cancer chemotherapy treatment
Padmanabhan, R., Meskin, N., & Haddad, W. M. (2017) · Mathematical Biosciences · doi:10.1016/j.mbs.2017.08.004 · Cited by 133
Metadata
- Authors
- Baleanu, D., Jajarmi, A., Sajjadi, S. S., & Mozyrska, D.
- Venue
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Publisher
- AIP Publishing
- Published
- 2019-08-01
- Volume
- 29
- Issue
- 8
- Pages
- 083127-083127
- ISSN
- 1054-1500 (ISSN-L)
- 1089-7682
- OpenAlex
- W2970054927
- Cited by
- 357
- References
- 18
- FWCI
- 26.55
- Type
- journal article
- Language
- en
- Open access
- closed
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: A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. https://app.cochat.ai/papers/10.1063/1.5096159
- The paper
- Baleanu, D., Jajarmi, A., Sajjadi, S. S., & Mozyrska, D. (2019). A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. Chaos: An Interdisciplinary Journal of Nonlinear Science. https://doi.org/10.1063/1.5096159
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.
