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Real world applications of fractional models by Atangana–Baleanu fractional derivative

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  • Bas, Erdal
  • Ozarslan, Ramazan

Abstract

In this study, some modeling problems, Newton,’s law of cooling, population growth, logistic equation, blood alcohol model, are considered by Atangana–Baleanu fractional derivative. Analytical solutions are obtained by Laplace transform and results are simulated by figures under different orders. Atangana-Baleanu fractional derivative gives more precise results to the derivative with exponential kernel because of having fractional order, and so it is a generalized version of the derivative with exponential kernel.

Suggested Citation

  • Bas, Erdal & Ozarslan, Ramazan, 2018. "Real world applications of fractional models by Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 121-125.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:121-125
    DOI: 10.1016/j.chaos.2018.09.019
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    References listed on IDEAS

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    1. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Cattani, Carlo & Ciancio, Armando, 2016. "On the fractal distribution of primes and prime-indexed primes by the binary image analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 222-229.
    4. Sun, HongGuang & Hao, Xiaoxiao & Zhang, Yong & Baleanu, Dumitru, 2017. "Relaxation and diffusion models with non-singular kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 590-596.
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    Citations

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    Cited by:

    1. Balasubramaniam, P., 2022. "Solvability of Atangana-Baleanu-Riemann (ABR) fractional stochastic differential equations driven by Rosenblatt process via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Balasubramaniam, P., 2021. "Controllability of semilinear noninstantaneous impulsive ABC neutral fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Oxygen-plankton model under the effect of global warming with nonsingular fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Turkyilmazoglu, Mustafa & Altanji, Mohamed, 2023. "Fractional models of falling object with linear and quadratic frictional forces considering Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Acay, Bahar & Bas, Erdal & Abdeljawad, Thabet, 2020. "Fractional economic models based on market equilibrium in the frame of different type kernels," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    6. Aimene, D. & Baleanu, D. & Seba, D., 2019. "Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 51-57.
    7. 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).
    8. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.

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