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An Alpha‐Beta Phase Diagram Representation of the Zeros and Properties of the Mittag‐Leffler Function

Author

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  • John W. Hanneken
  • B. N. Narahari Achar
  • David M. Vaught

Abstract

A significant advance in characterizing the nature of the zeros and organizing the Mittag‐Leffler functions into phases according to their behavior is presented. Regions have been identified in the domain of α and β where the Mittag‐Leffler functions Eα,β(z) have not only the same type of zeros but also exhibit similar functional behavior, and this permits the establishment of an α‐β phase diagram.

Suggested Citation

  • John W. Hanneken & B. N. Narahari Achar & David M. Vaught, 2013. "An Alpha‐Beta Phase Diagram Representation of the Zeros and Properties of the Mittag‐Leffler Function," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:421685
    DOI: 10.1155/2013/421685
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    References listed on IDEAS

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    1. Duan, Jun-Sheng & Wang, Zhong & Liu, Yu-Lu & Qiu, Xiang, 2013. "Eigenvalue problems for fractional ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 46-53.
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