Year 2023,
Volume: 5 Issue: 1, 27 - 33, 31.03.2023
Muhammad Sinan
,
Kamal Shah
,
Thabet Abdeljawad
,
Ali Akgul
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
Muhammad Sinan
,
Kamal Shah
,
Thabet Abdeljawad
,
Ali Akgul
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.