IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v256y2015icp851-859.html
   My bibliography  Save this article

A general form of the generalized Taylor’s formula with some applications

Author

Listed:
  • El-Ajou, Ahmad
  • Abu Arqub, Omar
  • Al-Smadi, Mohammed

Abstract

In this article, a new general form of fractional power series is introduced in the sense of the Caputo fractional derivative. Using this approach some results of the classical power series are circulated and proved to this fractional power series, whilst a new general form of the generalized Taylor’s formula is also obtained. Some applications including fractional power series solutions for higher-order linear fractional differential equations subject to given nonhomogeneous initial conditions are provided and analyzed to guarantee and to confirm the performance of the proposed results. The results reveal that the new fractional expansion is very effective, straightforward, and powerful for formulating the exact solutions in the form of a rapidly convergent series with easily computable components.

Suggested Citation

  • El-Ajou, Ahmad & Abu Arqub, Omar & Al-Smadi, Mohammed, 2015. "A general form of the generalized Taylor’s formula with some applications," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 851-859.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:851-859
    DOI: 10.1016/j.amc.2015.01.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031500048X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.01.034?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. Tarasov, Vasily E. & Zaslavsky, George M., 2005. "Fractional Ginzburg–Landau equation for fractal media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 249-261.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Alquran, Marwan & Yousef, Feras & Alquran, Farah & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2021. "Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 62-76.
    2. Aylin Bayrak, Mine & Demir, Ali, 2018. "A new approach for space-time fractional partial differential equations by residual power series method," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 215-230.
    3. Ali, Khalid K. & Wazwaz, Abdul-Majid & Maneea, M., 2024. "Efficient solutions for fractional Tsunami shallow-water mathematical model: A comparative study via semi analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Mohammed Shqair & Ahmad El-Ajou & Mazen Nairat, 2019. "Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    5. Shadimetov, Kh.M. & Hayotov, A.R. & Nuraliev, F.A., 2016. "Optimal quadrature formulas of Euler–Maclaurin type," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 340-355.
    6. Jaradat, I. & Al-Dolat, M. & Al-Zoubi, K. & Alquran, M., 2018. "Theory and applications of a more general form for fractional power series expansion," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 107-110.
    7. Arqub, Omar Abu & Maayah, Banan, 2019. "Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 394-402.

    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. Hong Lu & Linlin Wang & Mingji Zhang, 2022. "Dynamics of Fractional Stochastic Ginzburg–Landau Equation Driven by Nonlinear Noise," Mathematics, MDPI, vol. 10(23), pages 1-36, November.
    2. Pavlos, G.P. & Karakatsanis, L.P. & Iliopoulos, A.C. & Pavlos, E.G. & Xenakis, M.N. & Clark, Peter & Duke, Jamie & Monos, D.S., 2015. "Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 188-209.
    3. Ivars, Salim B. & Botey, Muriel & Herrero, Ramon & Staliunas, Kestutis, 2023. "Stabilisation of spatially periodic states by non-Hermitian potentials," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Qiu, Yunli & Malomed, Boris A. & Mihalache, Dumitru & Zhu, Xing & Zhang, Li & He, Yingji, 2020. "Soliton dynamics in a fractional complex Ginzburg-Landau model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Korabel, Nickolay & Zaslavsky, George M., 2007. "Transition to chaos in discrete nonlinear Schrödinger equation with long-range interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 223-237.
    6. Mahmoud A. Zaky & Ahmed S. Hendy & Rob H. De Staelen, 2021. "Alikhanov Legendre—Galerkin Spectral Method for the Coupled Nonlinear Time-Space Fractional Ginzburg–Landau Complex System," Mathematics, MDPI, vol. 9(2), pages 1-22, January.
    7. Heydari, M.H. & Razzaghi, M., 2023. "Piecewise fractional Chebyshev cardinal functions: Application for time fractional Ginzburg–Landau equation with a non-smooth solution," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    8. Tarasov, Vasily E. & Zaslavsky, George M., 2007. "Fractional dynamics of systems with long-range space interaction and temporal memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 291-308.

    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:apmaco:v:256:y:2015:i:c:p:851-859. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.