IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v141y2020ics0960077920307360.html
   My bibliography  Save this article

Existence of positive solutions for weighted fractional order differential equations

Author

Listed:
  • Abdo, Mohammed S.
  • Abdeljawad, Thabet
  • Ali, Saeed M.
  • Shah, Kamal
  • Jarad, Fahd

Abstract

In this paper, we deliberate two classes of initial value problems for nonlinear fractional differential equations under a version weighted generalized of Caputo fractional derivative given by Jarad et al. (2020a) [25]. We get a formula for the solution through the equivalent fractional integral equations to the proposed problems. The existence and uniqueness of positive solutions have been obtained by using lower and upper solutions. The acquired results are demonstrated by building the upper and lower control functions of the nonlinear term with the aid of Banach and Schauder fixed point theorems. The acquired results are demonstrated by pertinent numerical examples along with the Bashforth Moulton prediction correction scheme and Matlab.

Suggested Citation

  • Abdo, Mohammed S. & Abdeljawad, Thabet & Ali, Saeed M. & Shah, Kamal & Jarad, Fahd, 2020. "Existence of positive solutions for weighted fractional order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307360
    DOI: 10.1016/j.chaos.2020.110341
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920307360
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110341?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. Atangana, Abdon, 2020. "Fractional discretization: The African’s tortoise walk," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Mamadou Diouf & Ndolane Sene, 2020. "Analysis of the Financial Chaotic Model with the Fractional Derivative Operator," Complexity, Hindawi, vol. 2020, pages 1-14, June.
    3. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    4. Erden, Samet & Sarikaya, Mehmet Zeki, 2016. "Generalized Pompeiu type inequalities for local fractional integrals and its applications," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 282-291.
    5. Abdo, Mohammed S. & Shah, Kamal & Wahash, Hanan A. & Panchal, Satish K., 2020. "On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(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. Almalahi, Mohammed A. & Panchal, Satish K. & Jarad, Fahd, 2021. "Stability results of positive solutions for a system of ψ -Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. 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).

    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. Nabi, Khondoker Nazmoon & Abboubakar, Hamadjam & Kumar, Pushpendra, 2020. "Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Akgül, Ali & Siddique, Imran, 2021. "Analysis of MHD Couette flow by fractal-fractional differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Khan, Zeshan Aslam & Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor, 2022. "Generalized fractional strategy for recommender systems with chaotic ratings behavior," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Gao, Fei & Li, Xiling & Li, Wenqin & Zhou, Xianjin, 2021. "Stability analysis of a fractional-order novel hepatitis B virus model with immune delay based on Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Riaz, M.B. & Iftikhar, N., 2020. "A comparative study of heat transfer analysis of MHD Maxwell fluid in view of local and nonlocal differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    9. Dlamini, A. & Doungmo Goufo, E.F., 2023. "Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    10. Mahmood, Tariq & ur Rahman, Mati & Arfan, Muhammad & Kayani, Sadaf-Ilyas & Sun, Mei, 2023. "Mathematical study of Algae as a bio-fertilizer using fractal–fractional dynamic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 207-222.
    11. Jiong Weng & Xiaojing Liu & Youhe Zhou & Jizeng Wang, 2022. "An Explicit Wavelet Method for Solution of Nonlinear Fractional Wave Equations," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    12. Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2022. "Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    13. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
    14. Sabermahani, Sedigheh & Ordokhani, Yadollah & Rahimkhani, Parisa, 2023. "Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    15. Luo, Chunyan & Wang, Hao & Du, Tingsong, 2020. "Fejér–Hermite–Hadamard type inequalities involving generalized h-convexity on fractal sets and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    16. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    17. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    18. Crokidakis, Nuno, 2020. "COVID-19 spreading in Rio de Janeiro, Brazil: Do the policies of social isolation really work?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    19. Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.
    20. Shloof, A.M. & Senu, N. & Ahmadian, A. & Salahshour, Soheil, 2021. "An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 415-435.

    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:141:y:2020:i:c:s0960077920307360. 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.