Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
|
|
---|---|---|
Article Number | 48 | |
Number of page(s) | 13 | |
DOI | https://doi.org/10.1051/mmnp/2021032 | |
Published online | 09 August 2021 |
- B. Ahmad, M. Alghanmi, S.K. Ntouyas and A. Alsaedi, Fractional differential equations involving generalized derivative with Stieltjes and fractional integral boundary conditions. Appl. Math. Lett. 84 (2018) 111–117. [Google Scholar]
- M. Al-Refai and T. Abdeljawad, Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel. Adv. Differ. Equ. 2017 (2017) 315. [Google Scholar]
- D. Baleanu, H. Mohammadi and S. Rezapour, A mathematical theoretical study of a particular system of Caputo–Fabrizio fractionaldifferential equations for the Rubella disease model. Adv. Differ. Equ. 2020 (2020) 1–19. [Google Scholar]
- D. Baleanu, G.-C. Wu and S.-D. Zeng, Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations. Chaos Solitons Fract. 102 (2017) 99–105. [Google Scholar]
- H.M. Baskonus and H. Bulut, On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method. Open Math. 13 (2015) 547–556. [Google Scholar]
- M. Benjemaa, Taylor’s formula involving generalized fractional derivatives. Appl. Math. Comput. 335 (2018) 182–195. [Google Scholar]
- M. Caputo and F. Mainardi, A new dissipation model based on memory mechanism. Pure Appl. Geophys. 91 (1971) 134–147. [Google Scholar]
- P. Chanprasopchai, I.M. Tang and P. Pongsumpun, Sir model for dengue disease with effect of dengue vaccination. Comput. Math. Methods Med. 2018 (2018) 9861572. [Google Scholar]
- M. Derouich, A. Boutayeb and E. Twizell, A model of dengue fever. BioMedical Eng. OnLine 2 (2003) 4. [Google Scholar]
- K. Diethelm, N.J. Ford and A.D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29 (2002) 3–22. [Google Scholar]
- H. El-Saka, The fractional-order SIS epidemic model with variable population size. J. Egypt. Math. Soc. 22 (2014) 50–54. [Google Scholar]
- A.N. Fall, S.N. Ndiaye and N. Sene, Black–Scholes option pricing equations described by the Caputo generalized fractional derivative. Chaos Solitons Fract. 125 (2019) 108–118. [Google Scholar]
- Z. Feng and J.X. Velasco-Hernández, Competitive exclusion in a vector-host model for the dengue fever. J. Math. Biol. 35 (1997) 523–544. [Google Scholar]
- J. Gómez-Aguilar, Chaos and multiple attractors in a fractal–fractional Shinriki’s oscillator model. Physica A 539 (2020) 122918. [Google Scholar]
- J.F. Gómez-Aguilar, M.G. López-López, V.M. Alvarado-Martínez, D. Baleanu and H. Khan, Chaos in a cancer model via fractional derivatives with exponential decay and Mittag-Leffler law. Entropy 19 (2017) 681. [Google Scholar]
- J.F. Gómez-Aguilar, V.F. Morales-Delgado, M.A. Taneco-Hernández, D. Baleanu, R.F. Escobar-Jiménez and M.M. Al Qurashi Analytical solutions of the electrical RLC circuit via Liouville–Caputo operators with local and non-local kernels. Entropy 18 (2016) 402. [Google Scholar]
- F. Jarad, T. Abdeljawad and D. Baleanu, On the generalized fractional derivatives and their Caputo modification. J. Nonlinear Sci. Appl. 10 (2017) 2607–2619. [Google Scholar]
- U.N. Katugampola, New approach to a generalized fractional integral. Appl. Math. Comput. 218 (2011) 860–865. [Google Scholar]
- U.N. Katugampola, A new approach to generalized fractional derivatives. Bull. Math. Anal. Appl. 6 (2014) 1–15. [Google Scholar]
- U.N. Katugampola, Existence and uniqueness results for a class of generalized fractional differential equations. Preprint arXiv:1411.5229 (2016). [Google Scholar]
- M. Khalid, M. Sultana and F.S. Khan, Numerical solution of SIR model of dengue fever. Int. J. Comput. Appl. 118 (21). [Google Scholar]
- A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Vol. 204 of Theory and applications of fractional differential equations. Elsevier Science Limited (2006). [Google Scholar]
- I. Koca and P. Yaprakdal, A new approach for nuclear family model with fractional order Caputo derivative. Appl. Math. Nonlinear Sci. 5 (2020) 393–404. [Google Scholar]
- S. Kumar, A new fractional modeling arising in engineering sciences and its analytical approximate solution. Alexandria Eng. J. 52 (2013) 813–819. [Google Scholar]
- S. Kumar, R. Kumar, R.P. Agarwal and B. Samet, A study of fractional Lotka-Volterra population model using Haar wavelet and Adams-Bashforth-Moulton methods. Math. Methods Appl. Sci. 43 (2020) 5564–5578. [Google Scholar]
- S. Kumar, K.S. Nisar, R. Kumar, C. Cattani and B. Samet, A new Rabotnov fractional-exponential function-based fractional derivative for diffusion equation under external force. Math. Methods Appl. Sci. 43 (2020) 4460–4471. [Google Scholar]
- S. Kumar, A. Kumar, S. Abbas, M. Al Qurashi and D. Baleanu, A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations. Adv. Differ. Equ. 2020 (2020) 1–18. [Google Scholar]
- S. Kumar, A. Kumar and Z.M. Odibat, A nonlinear fractional model to describe the population dynamics of two interacting species. Math. Methods Appl. Sci. 40 (2017) 4134–4148. [Google Scholar]
- C. Li, D. Qian and Y. Chen, On riemann-liouville and caputo derivatives. Discrete Dyn. Nature Soc. (2011). [Google Scholar]
- Z. Odibat and D. Baleanu, Numerical simulation of initial value problems with generalized Caputo-type fractional derivatives. Appl. Numer. Math. 156 (2020) 94–105. [Google Scholar]
- R. Ozarslan and E. Bas, Kinetic model for drying in frame of generalized fractional derivatives. Fractal Fract. 4 (2020) 17. [Google Scholar]
- I. Podlubny, Vol. 198 of Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier (1998). [Google Scholar]
- Y.M. Rangkuti, S. Side and M.S.M. Noorani, Numerical analytic solution of SIR model of dengue fever disease in south Sulawesi using homotopy perturbation method and variational iteration method. J. Math. Fund. Sci. 46 (2014) 91–105. [Google Scholar]
- K. Shah, F. Jarad and T. Abdeljawad, On a nonlinear fractional order model of dengue fever disease under Caputo-Fabrizio derivative. Alexandria Eng. J. 59 (2020) 2305–2313. [Google Scholar]
- A.S. Shaikh and K.S. Nisar, Transmission dynamics of fractional order typhoid fever model using Caputo–Fabrizio operator. Chaos Solitons Fract. 128 (2019) 355–365. [Google Scholar]
- Y. Shen, Mathematical models of dengue fever and measures to control it, Ph.D. dissertation, Florida State University Libraries (2014). [Google Scholar]
- S. Side and M.S.M. Noorani, A sir model for spread of dengue fever disease (simulation for south Sulawesi, Indonesia and Selangor, Malaysia). World J. Model. Simul. 9 (2013) 96–105. [Google Scholar]
- J. Singh, D. Kumar, M. Al Qurashi and D. Baleanu, A new fractional model for giving up smoking dynamics. Adv. Differ. Equ. 2017 (2017) 88. [Google Scholar]
- J. Singh, D. Kumar, Z. Hammouch and A. Atangana, A fractional epidemiological model for computer viruses pertaining to a new fractional derivative. Appl. Math. Comput. 316 (2018) 504–515. [Google Scholar]
- S. Ullah, M.A. Khan and M. Farooq, A new fractional model for the dynamics of the hepatitis B virus using the Caputo-Fabrizio derivative. Eur. Phys. J. Plus 133 (2018) 237. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.