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New numerical simulations for some real world problems with Atangana–Baleanu fractional derivative

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  • Gao, Wei
  • Ghanbari, Behzad
  • Baskonus, Haci Mehmet

Abstract

In this work, we introduce ABC-Caputo operator with ML kernel and its main characteristics are discussed. Viral diseases models for AIDS and Zika are considered, and finally, as third model, the macroeconomic model involving ABC fractional derivatives is investigated, respectively. It is presented that the AB Caputo derivatives satisfy the Lipschitz condition along with superposition property. The numerical methods for solving the fractional models are presented by means of ABC fractional derivative in a detailed manner. Finally the simulation results obtained in this paper according to the suitable values of parameters are also manifested.

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  • Gao, Wei & Ghanbari, Behzad & Baskonus, Haci Mehmet, 2019. "New numerical simulations for some real world problems with Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 34-43.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:34-43
    DOI: 10.1016/j.chaos.2019.07.037
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    4. Prakash, Amit & Kaur, Hardish, 2019. "Analysis and numerical simulation of fractional order Cahn–Allen model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 134-142.
    5. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
    6. Owolabi, Kolade M., 2019. "Behavioural study of symbiosis dynamics via the Caputo and Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 89-101.
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    14. Srivastava, H.M. & Dubey, V.P. & Kumar, R. & Singh, J. & Kumar, D. & Baleanu, D., 2020. "An efficient computational approach for a fractional-order biological population model with carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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    16. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    17. Kateryna Marynets, 2021. "Successive Approximation Technique in the Study of a Nonlinear Fractional Boundary Value Problem," Mathematics, MDPI, vol. 9(7), pages 1-19, March.
    18. Christopher Nicholas Angstmann & Byron Alexander Jacobs & Bruce Ian Henry & Zhuang Xu, 2020. "Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    19. Zafar, Zain Ul Abadin & Ali, Nigar & Baleanu, Dumitru, 2021. "Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    20. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    21. Panda, Sumati Kumari & Abdeljawad, Thabet & Ravichandran, C., 2020. "A complex valued approach to the solutions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation via fixed point method," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
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    23. Saad, Khaled M. & Srivastava, H.M. & Gómez-Aguilar, J.F., 2020. "A Fractional Quadratic autocatalysis associated with chemical clock reactions involving linear inhibition," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).

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