Theoretical and numerical investigation of a modified ABC fractional operator for the spread of polio under the effect of vaccination

Mati ur Rahman; Mehmet Yavuz; Muhammad Arfan; Adnan Sami; Mati ur Rahman; Mehmet Yavuz; Muhammad Arfan; Adnan Sami

doi:10.3934/biophy.2024007

AIMS Biophysics

2024, Volume 11, Issue 1: 97-120. doi: 10.3934/biophy.2024007

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Theoretical and numerical investigation of a modified ABC fractional operator for the spread of polio under the effect of vaccination

1.
School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu P.R.China
2.
Department of Computer Science and Mathematics, Lebanese American University, Beirut Lebanon
3.
Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, 42090 Konya, Türkiye
4.
Department of Mathematics, Environment & Sustainability Institute, College of Engineering, Mathematics & Physical Sciences, University of Exeter-Penryn Campus, TR10 9FE, UK
5.
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan

Received: 15 December 2023 Revised: 21 January 2024 Accepted: 31 January 2024 Published: 06 February 2024

The current manuscript investigates a model of the spread of polio under the condition of vaccination by using the novel modified Atangana-Baleanu-Caputo (mABC) fractional derivative. This problem has been studied for non-zero solutions under the modified operator. The series-type solution has been obtained through the application of a Laplace transformation, along with the decomposition technique and Adomian polynomial for the nonlinear terms. The qualitative analysis for the solution of the model has been tested by using fixed point theory. The stability of the solution is also crucial for a dynamical system; therefore, it was checked by using the T-Picard method. With the help of the approximate scheme, numerical simulations were conducted for the proposed model by using different fractional orders and transmission parameters. Based on the obtained positivity of the solutions and numerical stability, we have established the analysis of the mABC operator in the field of fractional calculus and other physical sciences.
- modified Atangana-Baleanu derivative,
- qualitative analysis,
- Laplace Adomian decomposition technique,
- polio model
Citation: Mati ur Rahman, Mehmet Yavuz, Muhammad Arfan, Adnan Sami. Theoretical and numerical investigation of a modified ABC fractional operator for the spread of polio under the effect of vaccination[J]. AIMS Biophysics, 2024, 11(1): 97-120. doi: 10.3934/biophy.2024007

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Abstract

The current manuscript investigates a model of the spread of polio under the condition of vaccination by using the novel modified Atangana-Baleanu-Caputo (mABC) fractional derivative. This problem has been studied for non-zero solutions under the modified operator. The series-type solution has been obtained through the application of a Laplace transformation, along with the decomposition technique and Adomian polynomial for the nonlinear terms. The qualitative analysis for the solution of the model has been tested by using fixed point theory. The stability of the solution is also crucial for a dynamical system; therefore, it was checked by using the T-Picard method. With the help of the approximate scheme, numerical simulations were conducted for the proposed model by using different fractional orders and transmission parameters. Based on the obtained positivity of the solutions and numerical stability, we have established the analysis of the mABC operator in the field of fractional calculus and other physical sciences.

Conflict of interest

The authors declare no conflict of interest.

References

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