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Fractal Fract
Volume 10
Issue 7
10.3390/fractalfract10070423
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Analytical Study of a Fractional Cancer Model with Oncolytic Virotherapy Using the Temimi–Ansari Method

by
Mohammed Shqair
1,*,
Mohammed Darras
2,
Zuhur Alqahtani
3,
Hadeel Albalawi
4 and
Ahmed Hagag
5
1
Department of Physics, College of Science, Zarqa University, Zarqa 13110, Jordan
2
Department of Mathematics, College of Science, Zarqa University, Zarqa 13110, Jordan
3
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4
Faculty of Applied Medical Sciences, The Hashemite University, Zarqa 13133, Jordan
5
Department of Mathematics and Computer Science, Faculty of Biotechnology, Sinai University, Ismailia 41636, Egypt
*
Author to whom correspondence should be addressed.
Fractal Fract. 2026, 10(7), 423; https://doi.org/10.3390/fractalfract10070423 (registering DOI)
Submission received: 15 May 2026 / Revised: 18 June 2026 / Accepted: 20 June 2026 / Published: 23 June 2026
(This article belongs to the Special Issue Analysis and Numerical Computations of Nonlinear Fractional and Classical Differential Equations)
Versions Notes

Abstract

We propose a fractional-order cancer virotherapy model based on Caputo derivatives to investigate the temporal interactions among tumor cells, viruses, and immune response components. The existence and uniqueness of the solutions for the proposed model are rigorously studied. The proposed model is capable of tracking the temporal dynamics of uninfected and infected cancer cells, free oncolytic virus, and several components of the immune response. To determine the analytical solutions of the resulting nonlinear fractional-order system, we utilize the Temimi–Ansari method (TAM). The convergence and accuracy of the method are confirmed via error analysis and numerical simulation carried out in MATHEMATICA. It is observed that the fractional order plays a prominent role in controlling the temporal dynamics of the cancer–virus–immune system, leading to a reduction in the number of infected cancer cells due to virotherapy. On the other hand, the immune response is vital for controlling cancer growth.
Keywords: caputo fractional derivative; oncolytic virotherapy; tumor–virus–immune dynamics; basic reproduction number; temimi–ansari method (TAM); existence and uniqueness caputo fractional derivative; oncolytic virotherapy; tumor–virus–immune dynamics; basic reproduction number; temimi–ansari method (TAM); existence and uniqueness

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MDPI and ACS Style

Shqair, M.; Darras, M.; Alqahtani, Z.; Albalawi, H.; Hagag, A. Analytical Study of a Fractional Cancer Model with Oncolytic Virotherapy Using the Temimi–Ansari Method. Fractal Fract. 2026, 10, 423. https://doi.org/10.3390/fractalfract10070423

AMA Style

Shqair M, Darras M, Alqahtani Z, Albalawi H, Hagag A. Analytical Study of a Fractional Cancer Model with Oncolytic Virotherapy Using the Temimi–Ansari Method. Fractal and Fractional. 2026; 10(7):423. https://doi.org/10.3390/fractalfract10070423

Chicago/Turabian Style

Shqair, Mohammed, Mohammed Darras, Zuhur Alqahtani, Hadeel Albalawi, and Ahmed Hagag. 2026. "Analytical Study of a Fractional Cancer Model with Oncolytic Virotherapy Using the Temimi–Ansari Method" Fractal and Fractional 10, no. 7: 423. https://doi.org/10.3390/fractalfract10070423

APA Style

Shqair, M., Darras, M., Alqahtani, Z., Albalawi, H., & Hagag, A. (2026). Analytical Study of a Fractional Cancer Model with Oncolytic Virotherapy Using the Temimi–Ansari Method. Fractal and Fractional, 10(7), 423. https://doi.org/10.3390/fractalfract10070423

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