KaydedilenlerDerginizi ekleyin

Dergiler / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 15 Issue: 2

A New Caputo-Fabrizio Hybrid Method for the Numerical Solution of Caputo-Fabrizio Fractional Epidemic Model

Aslı Alkan(FIRAT UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF MATHEMATICS, MATHEMATICS PR.)0000-0002-1036-7178
Halil Anaç(GUMUSHANE UNIVERSITY, TORUL VOCATIONAL SCHOOL, DEPARTMENT OF COMPUTER TECHNOLOGIES)0000-0002-1316-3947
Sayfa
—
Yayın Tarihi
2026-06-30
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The suggested method offers a versatile and effective analytical instrument for investigating real-world epidemic occurrences exhibiting long-term memory traits.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper presents a novel Caputo–Fabrizio hybrid numerical method for examining the dynamics of fractional epidemic models defined by memory effects and non-singular kernels.
📊
Temel Bulgular & Veri:The proposed method combines the Caputo–Fabrizio fractional derivative with a hybrid transform framework, facilitating the derivation of accurate and convergent approximate solutions for nonlinear epidemic systems.
💡
Sonuç & Katkı:The suggested method offers a versatile and effective analytical instrument for investigating real-world epidemic occurrences exhibiting long-term memory traits.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Epidemic model · Caputo-Fabrizio fractional operator · q-homotopy analysis transform method

Abstract

This paper presents a novel Caputo–Fabrizio hybrid numerical method for examining the dynamics of fractional epidemic models defined by memory effects and non-singular kernels. The proposed method combines the Caputo–Fabrizio fractional derivative with a hybrid transform framework, facilitating the derivation of accurate and convergent approximate solutions for nonlinear epidemic systems. The model's parameters are analyzed in relation to infection transmission and recovery dynamics, whereas the fractional order α regulates the magnitude of memory and genetic influences. Numerical simulations indicate that the novel hybrid method exhibits remarkable concordance with established results for integer-order scenarios, while showcasing enhanced precision, computing efficiency, and robustness in fractional contexts. The suggested method offers a versatile and effective analytical instrument for investigating real-world epidemic occurrences exhibiting long-term memory traits.

🔖

Bu Makaleye Atıf Yap

Alkan, A., Anaç, H. (2026). A New Caputo-Fabrizio Hybrid Method for the Numerical Solution of Caputo-Fabrizio Fractional Epidemic Model. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 15 Issue: 2. https://doi.org/10.17798/bitlisfen.1822685

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (32)

  1. J. D. Murray, Mathematical Biology: I. An Introduction, vol. 17. Berlin: Springer, 2007.
  2. E. D. Sontag, Lecture Notes on Mathematical Systems Biology. New Brunswick, NJ: Rutgers University, 2011.
  3. W. O. Kermack and A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proc. Roy. Soc. Lond. Ser. A, vol. 115, no. 772, pp. 700–721, 1927.
  4. H. M. Al-Smadi and N. G. Gumah, “On the homotopy analysis method for fractional SEIR epidemic model,” Res. J. Appl. Sci. Eng. Technol., vol. 7, no. 18, pp. 3809–3820, 2014. [Online]. Available: https://doi.org/10.19026/rjaset.7.738
  5. P. A. Naik, B. M. Yeolekar, S. Qureshi, N. Manhas, M. Ghoreishi, M. Yeolekar, et al., “Global analysis of a fractional-order hepatitis B virus model under immune response in the presence of cytokines,” Adv. Theory Simul., vol. 7, no. 12, 2024. [Online]. Available: https://doi.org/10.1002/adts.202400726
  6. J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus,” Commun. Nonlinear Sci. Numer. Simul., vol. 16, pp. 1140–1153, 2011.
  7. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus: Models and Numerical Methods. Singapore: World Scientific, 2012.
  8. R. Shah, A. S. Alshehry, and W. Weera, “A semi-analytical method to investigate fractional-order gas dynamics equations by Shehu transform,” Symmetry, vol. 14, p. 1458, 2022.
  9. S. Mukhtar, R. Shah, and S. Noor, “The numerical investigation of a fractional-order multi-dimensional model of Navier–Stokes equation via novel techniques,” Symmetry, vol. 14, p. 1102, 2022.
  10. N. A. Shah, Y. S. Hamed, K. M. Abualnaja, J. D. Chung, and A. Khan, “A comparative analysis of fractional-order Kaup–Kupershmidt equation within different operators,” Symmetry, vol. 14, p. 986, 2022.
  11. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier, 2006.
  12. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering. New York, NY: Academic Press, 1999.
  13. M. Caputo and M. Fabrizio, “A new definition of fractional derivative without singular kernel,” Progr. Fract. Differ. Appl., vol. 1, no. 2, pp. 73–85, 2015.
  14. A. Alkan, “Analysis of fractional advection equation with improved homotopy analysis method,” Osmaniye Korkut Ata Univ. J. Sci. Inst., vol. 7, no. 3, pp. 1215–1229, 2024.
  15. Alkan, “Improving homotopy analysis method with an optimal parameter for time-fractional Burgers equation,” Karamanoğlu Mehmetbey Univ. J. Eng. Nat. Sci., vol. 4, no. 2, pp. 117–134, 2022.
  16. Alkan, H. Bulut, T. Aktürk, Ö. Engin, and N. Güllüoğlu, “Analysis of nonlinear partial differential equation of traveling wave solutions with an effective method,” Sigma J. Eng. Nat. Sci., vol. 43, no. 2, pp. 487–494, 2025.
  17. S. J. Liao, “Comparison between the homotopy analysis method and homotopy perturbation method,” Appl. Math. Comput., vol. 169, pp. 1186–1194, 2005.
  18. S. J. Liao, “An optimal homotopy-analysis approach for strongly nonlinear differential equations,” Commun. Nonlinear Sci. Numer. Simul., vol. 15, pp. 2003–2016, 2010.
  19. A. Prakash, P. Veeresha, D. G. Prakasha, and M. Goyal, “A new efficient technique for solving fractional coupled Navier–Stokes equations using q-homotopy analysis transform method,” Pramana J. Phys., vol. 93, no. 1, p. 6, 2019.
  20. Losada and J. J. Nieto, “Properties of a new fractional derivative without singular kernel,” Progr. Fract. Differ. Appl., vol. 1, no. 2, pp. 87–92, 2015.
  21. Alkan and H. Anaç, “A new study on the Newell–Whitehead–Segel equation with Caputo–Fabrizio fractional derivative,” AIMS Math., vol. 9, no. 10, pp. 27979–27997, 2024.
  22. S. R. Kushare, D. P. Patil, and A. M. Takate, “The new integral transform, ‘Kushare transform’,” Int. J. Adv. Eng. Manag., vol. 3, no. 9, pp. 1589–1592, 2021.
  23. R. Prabakaran and T. Gunasekar, “Advancing cryptographic security with Kushare transform integration,” in Driving Transformative Technology Trends With Cloud Computing, Hershey, PA: IGI Global, 2024, pp. 224–242.
  24. N. A. Alshammari, N. S. Alharthi, A. M. Saeed, A. Khan, and A. H. Ganie, “Numerical solutions of a fractional order SEIR epidemic model of measles under Caputo fractional derivative,” PLoS One, vol. 20, no. 5, e0321089, 2025.
  25. Shah, R., Alkhezi, Y., & Alhamad, K. (2023). An analytical approach to solve the fractional Benney equation using the q-homotopy analysis transform method. Symmetry, 15(3), 669.
  26. Ali, K. K., Maneea, M., & Mohamed, M. S. (2023). Solving Nonlinear Fractional Models in Superconductivity Using the q‐Homotopy Analysis Transform Method. Journal of Mathematics, 2023(1), 6647375.
  27. Şengül, S., Bekiryazici, Z., & Merdan, M. (2024). Approximate solutions of fractional differential equations using optimal q-homotopy analysis method: A case study of Abel differential equations. Fractal and Fractional, 8(9), 533.
  28. Alkan, A., Bulut, H., & Aktürk, T. (2025). The Novel Numerical Solutions of Conformable Fractional Navier-Stokes Equation with the Robust Method. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 14(3), 1331-1347.
  29. Thakur, S., Singh, V., Kumar, A., Singh, A. K., & Srivastava, S. K. (2024). A time-fractional order hiv/aids epidemic model with q-hatm. International Journal of Applied and Computational Mathematics, 10(1), 26.
  30. Merdan, M., & Açikgöz, P. (2025). Investigation of fractional order covid-19 model with q-homotopy analysis transform method. Sigma, 43(2), 582-597.
  31. Kumar, A., Prakash, A., & Mehmet Baskonus, H. (2025). The epidemic COVID-19 model via Caputo–Fabrizio fractional operator. Waves in Random and Complex Media, 35(4), 6230-6244.
  32. Hanif, A., Kashif Butt, A. I., & Ahmad, W. (2023). Numerical approach to solve Caputo‐Fabrizio‐fractional model of corona pandemic with optimal control design and analysis. Mathematical Methods in the Applied Sciences, 46(8), 9751-9782.