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Analytical study of fractional Bratu-type equation arising in electro-spun organic nanofibers elaboration

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  • Dubey, Ved Prakash
  • Kumar, Rajnesh
  • Kumar, Devendra

Abstract

In this article, we present a hybrid analytical scheme, namely, homotopy perturbation transform method to achieve the solutions of the non-linear Bratu-type problem with fractional order derivatives. The Caputo type fractional derivatives are considered in the present article. He’s polynomial is used to tackle the nonlinearity which arise in our considered problem. Using the initial conditions, the numerical solutions of the problem are computed. The numerical procedure reveals that only a few iterations are needed for better approximation of the solutions, which illustrates the effectiveness and reliability of the method. Effects of fractional order derivatives on the solutions for various particular cases are depicted through graphs.

Suggested Citation

  • Dubey, Ved Prakash & Kumar, Rajnesh & Kumar, Devendra, 2019. "Analytical study of fractional Bratu-type equation arising in electro-spun organic nanofibers elaboration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 762-772.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:762-772
    DOI: 10.1016/j.physa.2019.01.094
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    References listed on IDEAS

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    1. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & Torres, L. & Escobar-Jiménez, R.F. & Valtierra-Rodríguez, M., 2017. "Synchronization of chaotic systems involving fractional operators of Liouville–Caputo type with variable-order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 1-21.
    2. Abbasbandy, S., 2007. "A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 257-260.
    3. Mingxu Yi & Kangwen Sun & Jun Huang & Lifeng Wang, 2013. "Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, December.
    4. Coronel-Escamilla, A. & Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Guerrero-Ramírez, G.V., 2016. "Triple pendulum model involving fractional derivatives with different kernels," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 248-261.
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    Cited by:

    1. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Jajarmi, Amin & Yusuf, Abdullahi & Baleanu, Dumitru & Inc, Mustafa, 2020. "A new fractional HRSV model and its optimal control: A non-singular operator approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    3. Rubayyi T. Alqahtani & Abdullahi Yusuf & Ravi P. Agarwal, 2021. "Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative," Mathematics, MDPI, vol. 9(6), pages 1-19, March.

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