IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v257y2015icp134-144.html
   My bibliography  Save this article

Initial value/boundary value problem for composite fractional relaxation equation

Author

Listed:
  • Mophou, G.
  • Tao, S.
  • Joseph, C.

Abstract

We consider initial value/boundary value problem for composite fractional relaxation equation involving Caputo fractional derivative of order 0<β<1. We prove by means of change of variable that this problem is reduced to initial value/boundary value problem for fractional diffusion equation involving Riemann–Liouville fractional derivative of order β=1-α. Then by means of eigenfunctions expansions, we establish the existence and uniqueness of solution.

Suggested Citation

  • Mophou, G. & Tao, S. & Joseph, C., 2015. "Initial value/boundary value problem for composite fractional relaxation equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 134-144.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:134-144
    DOI: 10.1016/j.amc.2014.09.081
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031401306X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.09.081?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. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    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. Bahaa, G.M., 2019. "Optimal control problem for variable-order fractional differential systems with time delay involving Atangana–Baleanu derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 129-142.
    2. Gisèle Mophou, 2017. "Optimal Control for Fractional Diffusion Equations with Incomplete Data," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 176-196, July.

    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. Marseguerra, Marzio & Zoia, Andrea, 2008. "Pre-asymptotic corrections to fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2668-2674.
    2. Wei, T. & Li, Y.S., 2018. "Identifying a diffusion coefficient in a time-fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 77-95.
    3. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    4. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    5. Marseguerra, M. & Zoia, A., 2008. "Monte Carlo evaluation of FADE approach to anomalous kinetics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 345-357.
    6. Kashfi Sadabad, Mahnaz & Jodayree Akbarfam, Aliasghar, 2021. "An efficient numerical method for estimating eigenvalues and eigenfunctions of fractional Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 547-569.
    7. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Alam, Mehboob & Shah, Dildar, 2021. "Hyers–Ulam stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    9. Guo, Gang & Chen, Bin & Zhao, Xinjun & Zhao, Fang & Wang, Quanmin, 2015. "First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 279-290.
    10. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    11. Yu, Xiangnan & Zhang, Yong & Sun, HongGuang & Zheng, Chunmiao, 2018. "Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 306-312.
    12. Lenzi, E.K. & Mendes, R.S. & Gonçalves, G. & Lenzi, M.K. & da Silva, L.R., 2006. "Fractional diffusion equation and Green function approach: Exact solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 215-226.
    13. Marseguerra, M. & Zoia, A., 2007. "Some insights in superdiffusive transport," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 1-14.
    14. Allahviranloo, T. & Gouyandeh, Z. & Armand, A., 2015. "Numerical solutions for fractional differential equations by Tau-Collocation method," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 979-990.
    15. Goel, Eti & Pandey, Rajesh K. & Yadav, S. & Agrawal, Om P., 2023. "A numerical approximation for generalized fractional Sturm–Liouville problem with application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 417-436.
    16. Alqhtani, Manal & Owolabi, Kolade M. & Saad, Khaled M. & Pindza, Edson, 2022. "Efficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    17. Khan, Sharon & Reynolds, Andy M., 2005. "Derivation of a Fokker–Planck equation for generalized Langevin dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 183-188.
    18. D’Ovidio, Mirko, 2012. "From Sturm–Liouville problems to fractional and anomalous diffusions," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3513-3544.
    19. Wang, Shaowei & Zhao, Moli & Li, Xicheng, 2011. "Radial anomalous diffusion in an annulus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3397-3403.
    20. Xian, Jun & Yan, Xiong-bin & Wei, Ting, 2020. "Simultaneous identification of three parameters in a time-fractional diffusion-wave equation by a part of boundary Cauchy data," Applied Mathematics and Computation, Elsevier, vol. 384(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:eee:apmaco:v:257:y:2015:i:c:p:134-144. 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.