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Fundamental solutions of the fractional Fresnel equation in the real half-line

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Listed:
  • Taneco-Hernández, M.A.
  • Morales-Delgado, V.F.
  • Gómez-Aguilar, J.F.

Abstract

The purpose of this paper is to offer a discussion on the fundamental solutions for the vibration fractional equation of rods semi-infinite (also called Fresnel equation). For this end, using the fractional derivative of Riemann–Liouville of order γ∈(1,2] with respect to the spatial variable, we solve boundary-value problems associated to the mentioned equation showing the connection with Brownian behavior and the heat equation. We obtain solutions for the fractional Fresnel equation using the unified transform method. In the intermediate of the investigation, we have solved generalized Cauchy problems associated with linear fractional Schrödinger equations with order γ.

Suggested Citation

  • Taneco-Hernández, M.A. & Morales-Delgado, V.F. & Gómez-Aguilar, J.F., 2019. "Fundamental solutions of the fractional Fresnel equation in the real half-line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 807-827.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:807-827
    DOI: 10.1016/j.physa.2019.01.105
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    References listed on IDEAS

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    1. Carr, Elliot J. & March, Nathan G., 2018. "Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 286-303.
    2. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    3. 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.
    4. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
    5. 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.
    6. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    7. Fernandez, Arran & Baleanu, Dumitru & Fokas, Athanassios S., 2018. "Solving PDEs of fractional order using the unified transform method," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 738-749.
    8. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    9. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
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