IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i23p4564-d991176.html
   My bibliography  Save this article

Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition

Author

Listed:
  • Ragwa S. E. Alatwi

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Abdulrahman F. Aljohani

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Abdelhalim Ebaid

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Hind K. Al-Jeaid

    (Department of Mathematical Sciences, Umm Al-Qura University, Makkah 715, Saudi Arabia)

Abstract

This paper considers a class of non-homogeneous fractional systems with harmonic terms by means of the Riemann–Liouville definition. Two different approaches are applied to obtain the dual solution of the studied class. The first approach uses the Laplace transform (LT) and the solution is given in terms of the Mittag-Leffler functions. The second approach avoids the LT and expresses the solution in terms of exponential and periodic functions which is analytic in the whole domain. The current methods determine the solution directly and efficiently. The results are applicable for other problems of higher order.

Suggested Citation

  • Ragwa S. E. Alatwi & Abdulrahman F. Aljohani & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2022. "Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition," Mathematics, MDPI, vol. 10(23), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4564-:d:991176
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/23/4564/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/23/4564/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    2. El Mehdi Lotfi & Houssine Zine & Delfim F. M. Torres & Noura Yousfi, 2022. "The Power Fractional Calculus: First Definitions and Properties with Applications to Power Fractional Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-10, October.
    3. Alderremy, A.A. & Saad, Khaled M. & Agarwal, Praveen & Aly, Shaban & Jain, Shilpi, 2020. "Certain new models of the multi space-fractional Gardner equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    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. Melike Kaplan & Rubayyi T. Alqahtani, 2023. "Exploration of New Solitons for the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model," Mathematics, MDPI, vol. 11(11), pages 1-9, June.

    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. Laila F. Seddek & Abdelhalim Ebaid & Essam R. El-Zahar & Mona D. Aljoufi, 2023. "Exact Solution of Non-Homogeneous Fractional Differential System Containing 2 n Periodic Terms under Physical Conditions," Mathematics, MDPI, vol. 11(15), pages 1-12, July.
    2. Ebrahem A. Algehyne & Musaad S. Aldhabani & Mounirah Areshi & Essam R. El-Zahar & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2023. "A Proposed Application of Fractional Calculus on Time Dilation in Special Theory of Relativity," Mathematics, MDPI, vol. 11(15), pages 1-11, July.
    3. Rehman, Attiq ul & Singh, Ram & Singh, Jagdev, 2022. "Mathematical analysis of multi-compartmental malaria transmission model with reinfection," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Akinlar, M.A. & Inc, Mustafa & Gómez-Aguilar, J.F. & Boutarfa, B., 2020. "Solutions of a disease model with fractional white noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Agarwal, Praveen & Singh, Ram & Rehman, Attiq ul, 2021. "Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Shaw, Pawan Kumar & Kumar, Sunil & Momani, Shaher & Hadid, Samir, 2022. "Dynamical analysis of fractional plant disease model with curative and preventive treatments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. Zehba Raizah & Rahat Zarin, 2023. "Advancing COVID-19 Understanding: Simulating Omicron Variant Spread Using Fractional-Order Models and Haar Wavelet Collocation," Mathematics, MDPI, vol. 11(8), pages 1-30, April.
    8. Xiaojun Zhou & Chunna Zhao & Yaqun Huang, 2023. "A Deep Learning Optimizer Based on Grünwald–Letnikov Fractional Order Definition," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    9. Rehman, Attiq ul & Singh, Ram & Agarwal, Praveen, 2021. "Modeling, analysis and prediction of new variants of covid-19 and dengue co-infection on complex network," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

    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:gam:jmathe:v:10:y:2022:i:23:p:4564-:d:991176. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.