IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v506y2018icp520-531.html
   My bibliography  Save this article

Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative

Author

Listed:
  • Inc, Mustafa
  • Yusuf, Abdullahi
  • Aliyu, Aliyu Isa
  • Baleanu, Dumitru

Abstract

This work presents analysis of the logarithmic-KdV equation involving new fractional operator called Atangana–Baleanu (AB) fractional derivative with Mittag-Leffler (ML) type kernel. The existence and uniqueness of the governing equation having AB fractional derivative with ML type kernel is proved with the aid of a fixed-point theorem. We present numerical simulations by using iterative algorithm. The effectiveness of various parameters and variables on the displacement are presented in Figures 1 and 2.

Suggested Citation

  • Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 520-531.
    • Handle: RePEc:eee:phsmap:v:506:y:2018:i:c:p:520-531
    DOI: 10.1016/j.physa.2018.04.092
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711830520X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.04.092?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. Singh, Jagdev & Kumar, Devendra & Nieto, Juan J., 2017. "Analysis of an El Nino-Southern Oscillation model with a new fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 109-115.
    2. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
    3. Abdulhameed, M. & Vieru, D. & Roslan, R., 2017. "Modeling electro-magneto-hydrodynamic thermo-fluidic transport of biofluids with new trend of fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 233-252.
    4. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Lie symmetry analysis, explicit solutions and conservation laws for the space–time fractional nonlinear evolution equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 371-383.
    5. Lashkarian, Elham & Reza Hejazi, S., 2017. "Group analysis of the time fractional generalized diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 572-579.
    6. Eslami, Mostafa, 2016. "Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 141-148.
    7. Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.
    8. Alkahtani, Badr Saad T. & Atangana, Abdon, 2016. "Analysis of non-homogeneous heat model with new trend of derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 566-571.
    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. Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Hosseini, Kamyar & Ilie, Mousa & Mirzazadeh, Mohammad & Yusuf, Abdullahi & Sulaiman, Tukur Abdulkadir & Baleanu, Dumitru & Salahshour, Soheil, 2021. "An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 248-260.
    3. Sania Qureshi & Norodin A. Rangaig & Dumitru Baleanu, 2019. "New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    4. Ahmed, Najma & Shah, Nehad Ali & Taherifar, Somaye & Zaman, F.D., 2021. "Memory effects and of the killing rate on the tumor cells concentration for a one-dimensional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    6. Mathiyalagan, K. & Renugadevi, T. & Nidhi, A. Shree & Ma, Yong-Ki & Cao, Jinde, 2022. "Boundary state feedback control for semilinear fractional-order reaction diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "On the analysis of semi-analytical solutions of Hepatitis B epidemic model under the Caputo-Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    9. Lu, D. & Osman, M.S. & Khater, M.M.A. & Attia, R.A.M. & Baleanu, D., 2020. "Analytical and numerical simulations for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo,Cu)) based on ternary alloys," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    10. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.

    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. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    2. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    3. Khalique, Chaudry Masood & Motsepa, Tanki, 2018. "Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 871-879.
    4. Abdulhameed, M. & Muhammad, M.M. & Gital, A.Y. & Yakubu, D.G. & Khan, I., 2019. "Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 42-71.
    5. Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    6. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    7. Stanislav Yu. Lukashchuk, 2022. "On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems," Mathematics, MDPI, vol. 10(13), pages 1-17, July.
    8. Singh, C.S. & Singh, Harendra & Singh, Somveer & Kumar, Devendra, 2019. "An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1440-1448.
    9. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    10. Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    11. Zahra, Waheed K. & Abdel-Aty, Mahmoud & Abidou, Diaa, 2020. "A fractional model for estimating the hole geometry in the laser drilling process of thin metal sheets," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    12. Zhang, Zhi-Yong & Li, Guo-Fang, 2020. "Lie symmetry analysis and exact solutions of the time-fractional biological population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    13. Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    14. Maiti, S. & Shaw, S. & Shit, G.C., 2020. "Caputo–Fabrizio fractional order model on MHD blood flow with heat and mass transfer through a porous vessel in the presence of thermal radiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    15. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    16. J. Kayalvizhi & A. G. Vijaya Kumar & Hakan F. Öztop & Ndolane Sene & Nidal H. Abu-Hamdeh, 2022. "Heat Transfer Enhancement through Thermodynamical Activity of H 2 O/Clay Nanofluid Flow over an Infinite Upright Plate with Caputo Fractional-Order Derivative," Energies, MDPI, vol. 15(16), pages 1-18, August.
    17. Nazir, Aqsa & Ahmed, Naveed & Khan, Umar & Mohyud-din, Syed Tauseef, 2020. "On stability of improved conformable model for studying the dynamics of a malnutrition community," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    18. Abdeljawad, Thabet & Atangana, Abdon & Gómez-Aguilar, J.F. & Jarad, Fahd, 2019. "On a more general fractional integration by parts formulae and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    19. Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.
    20. Cuahutenango-Barro, B. & Taneco-Hernández, M.A. & Gómez-Aguilar, J.F., 2018. "On the solutions of fractional-time wave equation with memory effect involving operators with regular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 283-299.

    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:phsmap:v:506:y:2018:i:c:p:520-531. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.