IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v107y2018icp161-169.html
   My bibliography  Save this article

Invariant subspaces admitted by fractional differential equations with conformable derivatives

Author

Listed:
  • Hashemi, M.S.

Abstract

There are various types of fractional derivatives in literature. One of the most natural and well-behaved fractional derivatives is recently introduced by the authors Khalil et al. [34], namely the conformable fractional derivative. In this paper, some more results about conformable fractional Laplace transform introduced by Abdeljawad [43] are investigated. The invariant subspace method is developed to get the exact solutions of various conformable time fractional differential equations. Finally, this theory is extended for the coupled system of conformable fractional differential equations, as well.

Suggested Citation

  • Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    • Handle: RePEc:eee:chsofr:v:107:y:2018:i:c:p:161-169
    DOI: 10.1016/j.chaos.2018.01.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791830002X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.01.002?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. Sahoo, S. & Saha Ray, S., 2016. "Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques (G′/G)-expansion method and improved (G′/G)-expansion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 265-282.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
    4. Huang, Qing & Zhdanov, Renat, 2014. "Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 110-118.
    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. Kaya, Guven & Kartal, Senol & Gurcan, Fuat, 2020. "Dynamical analysis of a discrete conformable fractional order bacteria population model in a microcosm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    2. Kheybari, Samad, 2021. "Numerical algorithm to Caputo type time–space fractional partial differential equations with variable coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 66-85.
    3. Hashemi, M.S., 2021. "A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    5. Ashpazzadeh, Elmira & Chu, Yu-Ming & Hashemi, Mir Sajjad & Moharrami, Mahsa & Inc, Mustafa, 2022. "Hermite multiwavelets representation for the sparse solution of nonlinear Abel’s integral equation," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    6. Martynyuk, Anatoliy A. & Stamov, Gani Tr. & Stamova, Ivanka M., 2020. "Fractional-like Hukuhara derivatives in the theory of set-valued differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    7. Hassan Eltayeb & Said Mesloub & Yahya T. Abdalla & Adem Kılıçman, 2019. "A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations," Mathematics, MDPI, vol. 7(10), pages 1-21, October.

    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. Hayman Thabet & Subhash Kendre & Dimplekumar Chalishajar, 2017. "New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-15, September.
    2. Jahanshahi, S. & Babolian, E. & Torres, D.F.M. & Vahidi, A.R., 2017. "A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 295-304.
    3. El-Dessoky Ahmed, M.M. & Altaf Khan, Muhammad, 2020. "Modeling and analysis of the polluted lakes system with various fractional approaches," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Seadawy, Aly R. & Ali, Asghar & Althobaiti, Saad & Sayed, Samy, 2021. "Propagation of wave solutions of nonlinear Heisenberg ferromagnetic spin chain and Vakhnenko dynamical equations arising in nonlinear water wave models," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Koca, Ilknur, 2018. "Efficient numerical approach for solving fractional partial differential equations with non-singular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 278-286.
    6. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
    7. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 171-179.
    8. Hammad, Hasanen A. & Alshehri, Maryam G., 2024. "Application of the Mittag-Leffler kernel in stochastic differential systems for approximating the controllability of nonlocal fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Sheikh, Nadeem Ahmad & Ali, Farhad & Khan, Ilyas & Gohar, Madeha, 2018. "A theoretical study on the performance of a solar collector using CeO2 and Al2O3 water based nanofluids with inclined plate: Atangana–Baleanu fractional model," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 135-142.
    11. Aimene, D. & Baleanu, D. & Seba, D., 2019. "Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 51-57.
    12. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    13. Jiang, Jingfei & Chen, Huatao & Guirao, Juan L.G. & Cao, Dengqing, 2019. "Existence of the solution and stability for a class of variable fractional order differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 269-274.
    14. Peng, Li & Zhou, Yong & Debbouche, Amar, 2019. "Approximation techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 234-241.
    15. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
    16. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    17. Sun, HongGuang & Hao, Xiaoxiao & Zhang, Yong & Baleanu, Dumitru, 2017. "Relaxation and diffusion models with non-singular kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 590-596.
    18. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    19. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    20. Fendzi-Donfack, Emmanuel & Kenfack-Jiotsa, Aurélien, 2023. "Extended Fan’s sub-ODE technique and its application to a fractional nonlinear coupled network including multicomponents — LC blocks," Chaos, Solitons & Fractals, Elsevier, vol. 177(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:chsofr:v:107:y:2018:i:c:p:161-169. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.