Research Article
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Year 2023, Volume: 5 Issue: 1, 27 - 33, 31.03.2023
https://doi.org/10.51537/chaos.1210461
An Erratum to this article was published on November 30, 2023. https://dergipark.org.tr/en/pub/chaos/issue/80150/1392836

Abstract

References

  • Abdo, M. S., K. Shah, H. A.Wahash, and S. K. Panchal, 2020 On a comprehensive model of the novel coronavirus (covid-19) under mittag-leffler derivative. Chaos, Solitons & Fractals 135: 109867.
  • Agarwal, R. P., V. Lakshmikantham, and J. J. Nieto, 2010 On the concept of solution for fractional differential equations with uncertainty. Nonlinear Analysis: Theory, Methods & Applications 72: 2859–2862.
  • Ahmad, S., A. Ullah, and A. Akgül, 2021a Investigating the complex behaviour of multi-scroll chaotic system with caputo fractalfractional operator. Chaos, Solitons & Fractals 146: 110900.
  • Ahmad, S., A. Ullah, A. Akgül, and M. De la Sen, 2021b A study of fractional order ambartsumian equation involving exponential decay kernel. AIMS Math 6: 9981–9997.
  • Ahmad, S., A. Ullah, M. Partohaghighi, S. Saifullah, A. Akgül, et al., 2021c Oscillatory and complex behaviour of caputo-fabrizio fractional order hiv-1 infection model. Aims Math 7: 4778–4792.
  • Alqahtani, R. T., S. Ahmad, and A. Akgül, 2021 Dynamical analysis of bio-ethanol production model under generalized nonlocal operator in caputo sense. Mathematics 9: 2370.
  • Arfan, M., H. Alrabaiah, M. U. Rahman, Y.-L. Sun, A. S. Hashim, et al., 2021 Investigation of fractal-fractional order model of covid-19 in pakistan under atangana-baleanu caputo (abc) derivative. Results in Physics 24: 104046.
  • Atangana, A., 2020 Extension of rate of change concept: from local to nonlocal operators with applications. Results in Physics 19: 103515.
  • Atangana, A. and S. ˙I. Araz, 2021 New concept in calculus: Piecewise differential and integral operators. Chaos, Solitons & Fractals 145: 110638.
  • Atangana, A. and S.˙I ˘gret Araz, 2020 Mathematical model of covid- 19 spread in turkey and south africa: theory, methods, and applications. Advances in Difference Equations 2020: 1–89.
  • Chitnis, N., J. M. Hyman, and J. M. Cushing, 2008 Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bulletin of mathematical biology 70: 1272–1296.
  • Doungmo Goufo, E. F., 2015 A biomathematical view on the fractional dynamics of cellulose degradation. Fractional Calculus and Applied Analysis 18: 554–564.
  • Doungmo Goufo, E. F., 2016 Application of the caputo-fabrizio fractional derivative without singular kernel to korteweg-de vries-burgers equation. Mathematical Modelling and Analysis 21: 188–198.
  • Grace, S., R. Agarwal, P.Wong, and A. Zafer, 2012 On the oscillation of fractional differential equations. Fractional Calculus and Applied Analysis 15: 222–231.
  • Hajiseyedazizi, S. N., M. E. Samei, J. Alzabut, and Y. ming Chu, 2021 On multi-step methods for singular fractional q-integrodifferential equations. Open Mathematics 19: 1378–1405.
  • Hilfer, R. et al., 2008 Threefold introduction to fractional derivatives. Anomalous transport: Foundations and applications pp. 17–73.
  • Machado, J. T., V. Kiryakova, and F. Mainardi, 2011 Recent history of fractional calculus. Communications in nonlinear science and numerical simulation 16: 1140–1153.
  • Nawaz, Y., M. S. Arif, and W. Shatanawi, 2022 A new numerical scheme for time fractional diffusive seair model with non-linear incidence rate: An application to computational biology. Fractal and Fractional 6: 78.
  • Ojo, M. M. and E. F. D. Goufo, 2022 Modeling, analyzing and simulating the dynamics of lassa fever in nigeria. Journal of the Egyptian Mathematical Society 30: 1.
  • Ojo, M. M. and E. F. D. Goufo, 2023 The impact of covid-19 on a malaria dominated region: A mathematical analysis and simulations. Alexandria Engineering Journal 65: 23–39.
  • Rahman, F., A. Ali, and S. Saifullah, 2021 Analysis of timefractional ϕ 4-equation with singular and non-singular kernels. International Journal of Applied and Computational Mathematics 7: 192.
  • Saifullah, S., A. Ali, and E. F. D. Goufo, 2021 Investigation of complex behaviour of fractal fractional chaotic attractor with mittag-leffler kernel. Chaos, Solitons & Fractals 152: 111332.
  • Saifullah, S., A. Ali, and Z. A. Khan, 2022 Analysis of nonlinear time-fractional klein-gordon equation with power law kernel. AIMS Math 7: 5275–5290.
  • Shah, K., B. Abdalla, T. Abdeljawad, and R. Gul, 2023 Analysis of multipoint impulsive problem of fractional-order differential equations. Boundary Value Problems 2023: 1–17.
  • Shah, K., T. Abdeljawad, B. Abdalla, and M. S. Abualrub, 2022a Utilizing fixed point approach to investigate piecewise equations with non-singular type derivative. AIMS Math 7: 14614–14630.
  • Shah, K., T. Abdeljawad, and A. Ali, 2022b Mathematical analysis of the cauchy type dynamical system under piecewise equations with caputo fractional derivative. Chaos, Solitons & Fractals 161: 112356.
  • Shah, K., T. Abdeljawad, and H. Alrabaiah, 2022c On coupled system of drug therapy via piecewise equations. Fractals 30: 2240206.
  • Shatanawi, W., M. S. Abdo, M. A. Abdulwasaa, K. Shah, S. K. Panchal, et al., 2021 A fractional dynamics of tuberculosis (tb) model in the frame of generalized atangana–baleanu derivative. Results in Physics 29: 104739.
  • Zhou, H., J. Alzabut, and L. Yang, 2017 On fractional langevin differential equations with anti-periodic boundary conditions. The European Physical Journal Special Topics 226: 3577–3590.

Analysis of Nonlinear Mathematical Model of COVID-19 via Fractional-Order Piecewise Derivative

Year 2023, Volume: 5 Issue: 1, 27 - 33, 31.03.2023
https://doi.org/10.51537/chaos.1210461
An Erratum to this article was published on November 30, 2023. https://dergipark.org.tr/en/pub/chaos/issue/80150/1392836

Abstract

Short memory and long memory terms are excellently explained using the concept of piecewise fractional order derivatives. In this research work, we investigate dynamical systems addressing COVID-19 under piecewise equations with fractional order derivative (FOD). Here, we study the sensitivity of the proposed model by using some tools from the nonlinear analysis. Additionally, we develop a numerical scheme to simulate the model against various fractional orders by using Matlab 2016. All the results are presented graphically.

References

  • Abdo, M. S., K. Shah, H. A.Wahash, and S. K. Panchal, 2020 On a comprehensive model of the novel coronavirus (covid-19) under mittag-leffler derivative. Chaos, Solitons & Fractals 135: 109867.
  • Agarwal, R. P., V. Lakshmikantham, and J. J. Nieto, 2010 On the concept of solution for fractional differential equations with uncertainty. Nonlinear Analysis: Theory, Methods & Applications 72: 2859–2862.
  • Ahmad, S., A. Ullah, and A. Akgül, 2021a Investigating the complex behaviour of multi-scroll chaotic system with caputo fractalfractional operator. Chaos, Solitons & Fractals 146: 110900.
  • Ahmad, S., A. Ullah, A. Akgül, and M. De la Sen, 2021b A study of fractional order ambartsumian equation involving exponential decay kernel. AIMS Math 6: 9981–9997.
  • Ahmad, S., A. Ullah, M. Partohaghighi, S. Saifullah, A. Akgül, et al., 2021c Oscillatory and complex behaviour of caputo-fabrizio fractional order hiv-1 infection model. Aims Math 7: 4778–4792.
  • Alqahtani, R. T., S. Ahmad, and A. Akgül, 2021 Dynamical analysis of bio-ethanol production model under generalized nonlocal operator in caputo sense. Mathematics 9: 2370.
  • Arfan, M., H. Alrabaiah, M. U. Rahman, Y.-L. Sun, A. S. Hashim, et al., 2021 Investigation of fractal-fractional order model of covid-19 in pakistan under atangana-baleanu caputo (abc) derivative. Results in Physics 24: 104046.
  • Atangana, A., 2020 Extension of rate of change concept: from local to nonlocal operators with applications. Results in Physics 19: 103515.
  • Atangana, A. and S. ˙I. Araz, 2021 New concept in calculus: Piecewise differential and integral operators. Chaos, Solitons & Fractals 145: 110638.
  • Atangana, A. and S.˙I ˘gret Araz, 2020 Mathematical model of covid- 19 spread in turkey and south africa: theory, methods, and applications. Advances in Difference Equations 2020: 1–89.
  • Chitnis, N., J. M. Hyman, and J. M. Cushing, 2008 Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bulletin of mathematical biology 70: 1272–1296.
  • Doungmo Goufo, E. F., 2015 A biomathematical view on the fractional dynamics of cellulose degradation. Fractional Calculus and Applied Analysis 18: 554–564.
  • Doungmo Goufo, E. F., 2016 Application of the caputo-fabrizio fractional derivative without singular kernel to korteweg-de vries-burgers equation. Mathematical Modelling and Analysis 21: 188–198.
  • Grace, S., R. Agarwal, P.Wong, and A. Zafer, 2012 On the oscillation of fractional differential equations. Fractional Calculus and Applied Analysis 15: 222–231.
  • Hajiseyedazizi, S. N., M. E. Samei, J. Alzabut, and Y. ming Chu, 2021 On multi-step methods for singular fractional q-integrodifferential equations. Open Mathematics 19: 1378–1405.
  • Hilfer, R. et al., 2008 Threefold introduction to fractional derivatives. Anomalous transport: Foundations and applications pp. 17–73.
  • Machado, J. T., V. Kiryakova, and F. Mainardi, 2011 Recent history of fractional calculus. Communications in nonlinear science and numerical simulation 16: 1140–1153.
  • Nawaz, Y., M. S. Arif, and W. Shatanawi, 2022 A new numerical scheme for time fractional diffusive seair model with non-linear incidence rate: An application to computational biology. Fractal and Fractional 6: 78.
  • Ojo, M. M. and E. F. D. Goufo, 2022 Modeling, analyzing and simulating the dynamics of lassa fever in nigeria. Journal of the Egyptian Mathematical Society 30: 1.
  • Ojo, M. M. and E. F. D. Goufo, 2023 The impact of covid-19 on a malaria dominated region: A mathematical analysis and simulations. Alexandria Engineering Journal 65: 23–39.
  • Rahman, F., A. Ali, and S. Saifullah, 2021 Analysis of timefractional ϕ 4-equation with singular and non-singular kernels. International Journal of Applied and Computational Mathematics 7: 192.
  • Saifullah, S., A. Ali, and E. F. D. Goufo, 2021 Investigation of complex behaviour of fractal fractional chaotic attractor with mittag-leffler kernel. Chaos, Solitons & Fractals 152: 111332.
  • Saifullah, S., A. Ali, and Z. A. Khan, 2022 Analysis of nonlinear time-fractional klein-gordon equation with power law kernel. AIMS Math 7: 5275–5290.
  • Shah, K., B. Abdalla, T. Abdeljawad, and R. Gul, 2023 Analysis of multipoint impulsive problem of fractional-order differential equations. Boundary Value Problems 2023: 1–17.
  • Shah, K., T. Abdeljawad, B. Abdalla, and M. S. Abualrub, 2022a Utilizing fixed point approach to investigate piecewise equations with non-singular type derivative. AIMS Math 7: 14614–14630.
  • Shah, K., T. Abdeljawad, and A. Ali, 2022b Mathematical analysis of the cauchy type dynamical system under piecewise equations with caputo fractional derivative. Chaos, Solitons & Fractals 161: 112356.
  • Shah, K., T. Abdeljawad, and H. Alrabaiah, 2022c On coupled system of drug therapy via piecewise equations. Fractals 30: 2240206.
  • Shatanawi, W., M. S. Abdo, M. A. Abdulwasaa, K. Shah, S. K. Panchal, et al., 2021 A fractional dynamics of tuberculosis (tb) model in the frame of generalized atangana–baleanu derivative. Results in Physics 29: 104739.
  • Zhou, H., J. Alzabut, and L. Yang, 2017 On fractional langevin differential equations with anti-periodic boundary conditions. The European Physical Journal Special Topics 226: 3577–3590.
There are 29 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Muhammad Sinan 0000-0003-2177-3806

Kamal Shah 0000-0002-8851-4844

Thabet Abdeljawad 0000-0002-8889-3768

Ali Akgul 0000-0001-9832-1424

Publication Date March 31, 2023
Published in Issue Year 2023 Volume: 5 Issue: 1

Cite

APA Sinan, M., Shah, K., Abdeljawad, T., Akgul, A. (2023). Analysis of Nonlinear Mathematical Model of COVID-19 via Fractional-Order Piecewise Derivative. Chaos Theory and Applications, 5(1), 27-33. https://doi.org/10.51537/chaos.1210461

Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830 28903   

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