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Novel technique of Atangana and Baleanu for heat dissipation in transmission line of electrical circuit

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  • Abro, Kashif Ali
  • Khan, Ilyas
  • Nisar, Kottakkaran Sooppy

Abstract

The new idea of Atangana and Baleanu introduced recently for fractional derivatives has received tremendous attention from researchers of various fields. However, this idea has not been applied for heat dissipation in transmission line of electrical circuit. Although the phenomenon of heat dissipation potentially damages the electrical devices which leads to catastrophic failure and shortens the life expectancy of costly electrical components. This manuscript signifies an electro-analog model of fractional diffusion process which enables to simulate heat dissipation in circuit board. The modeling of the problem has been established through modern operators of fractional calculus via the governing differential equation. By invoking Laplace transform on fractional governing equation of heat dissipation in transmission line of circuit, the analytic solutions are investigated through the exponential and Mittage Leffler kernel of non-integer order differentiations. The duality of analytic solutions has been compared with Caputo–Fabrizio and Atangana–Baleanu fractional differentiations graphically using embedded pertinent parameters. The comparison of both approaches of fractional differentiations has disclosed the heat transfer of circuit board and diffusion process with dissipation vividly.

Suggested Citation

  • Abro, Kashif Ali & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2019. "Novel technique of Atangana and Baleanu for heat dissipation in transmission line of electrical circuit," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 40-45.
    • Handle: RePEc:eee:chsofr:v:129:y:2019:i:c:p:40-45
    DOI: 10.1016/j.chaos.2019.08.001
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    References listed on IDEAS

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    1. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    2. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    3. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    4. Sierociuk, Dominik & Skovranek, Tomas & Macias, Michal & Podlubny, Igor & Petras, Ivo & Dzielinski, Andrzej & Ziubinski, Pawel, 2015. "Diffusion process modeling by using fractional-order models," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 2-11.
    5. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    6. Gaoyang Li & Xiaohua Wang & Aijun Yang & Mingzhe Rong & Kang Yang, 2017. "Failure Prognosis of High Voltage Circuit Breakers with Temporal Latent Dirichlet Allocation," Energies, MDPI, vol. 10(11), pages 1-20, November.
    7. J. F. Gómez-Aguilar & J. E. Escalante-Martínez & C. Calderón-Ramón & L. J. Morales-Mendoza & M. Benavidez-Cruz & M. Gonzalez-Lee, 2016. "Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-15, May.
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    Cited by:

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    4. Liu, Kui & Wang, JinRong & Zhou, Yong & O’Regan, Donal, 2020. "Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).

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