IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i12p1929-1939.html
   My bibliography  Save this article

On the fractional counterpart of the higher-order equations

Author

Listed:
  • D’Ovidio, Mirko

Abstract

In this work, we study the solutions of some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be expressed by means of the transition laws of stable subordinators and their inverse processes. In particular, we establish connections between fractional and higher-order equations.

Suggested Citation

  • D’Ovidio, Mirko, 2011. "On the fractional counterpart of the higher-order equations," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1929-1939.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1929-1939
    DOI: 10.1016/j.spl.2011.08.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211002689
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2011.08.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hochberg, Kenneth J. & Orsingher, Enzo, 1994. "The arc-sine law and its analogs for processes governed by signed and complex measures," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 273-292, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Beghin, L. & Orsingher, E. & Ragozina, T., 2001. "Joint distributions of the maximum and the process for higher-order diffusions," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 71-93, July.
    2. Lachal, Aimé, 2014. "First exit time from a bounded interval for pseudo-processes driven by the equation ∂/∂t=(−1)N−1∂2N/∂x2N," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1084-1111.
    3. Y. Nikitin & E. Orsingher, 2000. "On Sojourn Distributions of Processes Related to Some Higher-Order Heat-Type Equations," Journal of Theoretical Probability, Springer, vol. 13(4), pages 997-1012, October.
    4. Beghin, Luisa & Hochberg, Kenneth J. & Orsingher, Enzo, 2000. "Conditional maximal distributions of processes related to higher-order heat-type equations," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 209-223, February.
    5. Bonaccorsi, Stefano & Mazzucchi, Sonia, 2015. "High order heat-type equations and random walks on the complex plane," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 797-818.
    6. Beghin, L. & Orsingher, E., 2005. "The distribution of the local time for "pseudoprocesses" and its connection with fractional diffusion equations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 1017-1040, June.
    7. Aimé Lachal, 2012. "A Survey on the Pseudo-process Driven by the High-order Heat-type Equation $\boldsymbol{\partial/\partial t=\pm\partial^N\!/\partial x^N}$ Concerning the Hitting and Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 549-566, September.
    8. Bonaccorsi, Stefano & Calcaterra, Craig & Mazzucchi, Sonia, 2017. "An Itô calculus for a class of limit processes arising from random walks on the complex plane," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2816-2840.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1929-1939. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.