IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v390y2021ics0096300320305452.html
   My bibliography  Save this article

Explicit analytical solutions of incommensurate fractional differential equation systems

Author

Listed:
  • Huseynov, Ismail T.
  • Ahmadova, Arzu
  • Fernandez, Arran
  • Mahmudov, Nazim I.

Abstract

Fractional differential equations have been studied due to their applications in modelling, and solved using various mathematical methods. Systems of fractional differential equations are also used, for example in the study of electric circuits, but they are more difficult to analyse mathematically. We present explicit solutions for several families of such systems, both homogeneous and inhomogeneous cases, both commensurate and incommensurate. The results can be written, in several interesting special cases, in terms of a recently defined bivariate Mittag-Leffler function and the associated operators of fractional calculus.

Suggested Citation

  • Huseynov, Ismail T. & Ahmadova, Arzu & Fernandez, Arran & Mahmudov, Nazim I., 2021. "Explicit analytical solutions of incommensurate fractional differential equation systems," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305452
    DOI: 10.1016/j.amc.2020.125590
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320305452
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125590?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. Ahmadova, Arzu & Mahmudov, Nazim I., 2020. "Existence and uniqueness results for a class of fractional stochastic neutral differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Fernandez, Arran & Baleanu, Dumitru & Fokas, Athanassios S., 2018. "Solving PDEs of fractional order using the unified transform method," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 738-749.
    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. Simon, S. Gimnitz & Bira, B. & Zeidan, Dia, 2023. "Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Mahmudov, Nazim I. & Aydın, Mustafa, 2021. "Representation of solutions of nonhomogeneous conformable fractional delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Kürt, Cemaliye & Fernandez, Arran & Özarslan, Mehmet Ali, 2023. "Two unified families of bivariate Mittag-Leffler functions," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    4. Du, Feifei & Lu, Jun-Guo, 2021. "Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

    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. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    3. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Linna Liu & Feiqi Deng & Boyang Qu & Yanhong Meng, 2022. "Fundamental Properties of Nonlinear Stochastic Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    5. Ahmadova, Arzu & Mahmudov, Nazim I., 2021. "Strong convergence of a Euler–Maruyama method for fractional stochastic Langevin equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 429-448.
    6. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    7. Seyfeddine Moualkia & Yong Xu, 2021. "On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    8. Taneco-Hernández, M.A. & Morales-Delgado, V.F. & Gómez-Aguilar, J.F., 2019. "Fundamental solutions of the fractional Fresnel equation in the real half-line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 807-827.
    9. Ahmadova, Arzu & Mahmudov, Nazim I., 2021. "Ulam–Hyers stability of Caputo type fractional stochastic neutral differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).
    10. Xu, Shuli & Feng, Yuqiang & Jiang, Jun & Nie, Na, 2022. "A variation of constant formula for Caputo fractional stochastic differential equations with jump–diffusion," Statistics & Probability Letters, Elsevier, vol. 185(C).
    11. Upadhyay, Anjali & Kumar, Surendra, 2023. "The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    12. Abdelhamid Mohammed Djaouti & Zareen A. Khan & Muhammad Imran Liaqat & Ashraf Al-Quran, 2024. "Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the L p Space with the Framework of the Ψ-Caputo Derivative," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    13. Dumitru Baleanu & Arran Fernandez & Ali Akgül, 2020. "On a Fractional Operator Combining Proportional and Classical Differintegrals," Mathematics, MDPI, vol. 8(3), pages 1-13, March.

    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:390:y:2021:i:c:s0096300320305452. 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.