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A new fractional derivative involving the normalized sinc function without singular kernel

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Abstract

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, P.R. China

    Xiao-Jun Yang & Feng Gao

  2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, P.R. China

    Xiao-Jun Yang & Feng Gao

  3. Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. António Bernardino de Almeida, 4249-015, Porto, Portugal

    J. A. Tenreiro Machado

  4. Department of Mathematics, Cankya University, Ogretmenler Cad. 14, Balgat, 06530, Ankara, Turkey

    Dumitru Baleanu

  5. Institute of Space Sciences, Magurele, Bucharest, Romania

    Dumitru Baleanu

Authors
  1. Xiao-Jun Yang
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  2. Feng Gao
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  3. J. A. Tenreiro Machado
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  4. Dumitru Baleanu
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Correspondence to Xiao-Jun Yang.

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Yang, XJ., Gao, F., Tenreiro Machado, J.A. et al. A new fractional derivative involving the normalized sinc function without singular kernel. Eur. Phys. J. Spec. Top. 226, 3567–3575 (2017). https://doi.org/10.1140/epjst/e2018-00020-2

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  • DOI: https://doi.org/10.1140/epjst/e2018-00020-2

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