IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/406910.html
   My bibliography  Save this article

On Delta and Nabla Caputo Fractional Differences and Dual Identities

Author

Listed:
  • Thabet Abdeljawad

Abstract

We investigate two types of dual identities for Caputo fractional differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q -operator relates left and right fractional sums and differences. Two types of Caputo fractional differences are introduced; one of them (dual one) is defined so that it obeys the investigated dual identities. The relation between Riemann and Caputo fractional differences is investigated, and the delta and nabla discrete Mittag-Leffler functions are confirmed by solving Caputo type linear fractional difference equations. A nabla integration by parts formula is obtained for Caputo fractional differences as well.

Suggested Citation

  • Thabet Abdeljawad, 2013. "On Delta and Nabla Caputo Fractional Differences and Dual Identities," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, July.
    • Handle: RePEc:hin:jnddns:406910
    DOI: 10.1155/2013/406910
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/DDNS/2013/406910.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/DDNS/2013/406910.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/406910?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Abdeljawad, Thabet, 2018. "Different type kernel h−fractional differences and their fractional h−sums," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 146-156.
    2. Thabet Abdeljawad & Arran Fernandez, 2019. "On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    3. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    4. Qiushuang Wang & Run Xu, 2022. "On Hilfer Generalized Proportional Nabla Fractional Difference Operators," Mathematics, MDPI, vol. 10(15), pages 1-16, July.
    5. Mohammed, Pshtiwan Othman & Abdeljawad, Thabet & Hamasalh, Faraidun Kadir, 2021. "Discrete Prabhakar fractional difference and sum operators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Rashid, Saima & Sultana, Sobia & Jarad, Fahd & Jafari, Hossein & Hamed, Y.S., 2021. "More efficient estimates via ℏ-discrete fractional calculus theory and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    7. Almusawa, Musawa Yahya & Mohammed, Pshtiwan Othman, 2023. "Approximation of sequential fractional systems of Liouville–Caputo type by discrete delta difference operators," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    8. Rashid, Saima & Sultana, Sobia & Hammouch, Zakia & Jarad, Fahd & Hamed, Y.S., 2021. "Novel aspects of discrete dynamical type inequalities within fractional operators having generalized ℏ-discrete Mittag-Leffler kernels and application," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    9. Pshtiwan Othman Mohammed & Thabet Abdeljawad & Faraidun Kadir Hamasalh, 2021. "On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis," Mathematics, MDPI, vol. 9(11), pages 1-17, June.
    10. Abdeljawad, Thabet & Baleanu, Dumitru, 2017. "Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 106-110.
    11. Jiraporn Reunsumrit & Thanin Sitthiwirattham, 2020. "On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations," Mathematics, MDPI, vol. 8(4), pages 1-13, March.
    12. Suwan, Iyad & Abdeljawad, Thabet & Jarad, Fahd, 2018. "Monotonicity analysis for nabla h-discrete fractional Atangana–Baleanu differences," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 50-59.
    13. Kamsing Nonlaopon & Pshtiwan Othman Mohammed & Y. S. Hamed & Rebwar Salih Muhammad & Aram Bahroz Brzo & Hassen Aydi, 2022. "Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators," Mathematics, MDPI, vol. 10(10), pages 1-9, May.
    14. Jarunee Soontharanon & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2019. "A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line," Mathematics, MDPI, vol. 7(3), pages 1-22, March.
    15. Panda, Sumati Kumari & Vijayakumar, Velusamy & Nagy, A.M., 2023. "Complex-valued neural networks with time delays in the Lp sense: Numerical simulations and finite time stability," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    16. Cui, Xueke & Li, Hong-Li & Zhang, Long & Hu, Cheng & Bao, Haibo, 2023. "Complete synchronization for discrete-time fractional-order coupled neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnddns:406910. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.