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Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection

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Listed:
  • Wang, Ying
  • Liu, Lishan
  • Zhang, Xinguang
  • Wu, Yonghong

Abstract

Fractional order derivative is nonlocal which exhibits a long time memory behavior. With advantage of these, fractional order dynamic system models are more accurate than integer order ones in understanding the dynamic behavior of bioprocesses such as HIV infection. In this paper, we systematically study the existence of positive solutions of an abstract fractional semipositone differential system involving integral boundary conditions arising from the study of HIV infection models. By using the fixed point theorem in cone, some new results are established and an example is given to demonstrate the application of our main results.

Suggested Citation

  • Wang, Ying & Liu, Lishan & Zhang, Xinguang & Wu, Yonghong, 2015. "Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 312-324.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:312-324
    DOI: 10.1016/j.amc.2015.01.080
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    References listed on IDEAS

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    1. Jing Wu & Xinguang Zhang, 2012. "Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Wei Wang & Li Huang, 2012. "Existence of Positive Solution for Semipositone Fractional Differential Equations Involving Riemann‐Stieltjes Integral Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    2. Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.
    3. Sheng Zhang & Lijie Zhang & Bo Xu, 2019. "Rational Waves and Complex Dynamics: Analytical Insights into a Generalized Nonlinear Schrödinger Equation with Distributed Coefficients," Complexity, Hindawi, vol. 2019, pages 1-17, March.
    4. Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Du, Feifei & Lu, Jun-Guo, 2020. "Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    6. Ying Chen & Lishan Liu & Fang Wang, 2022. "Unified Approach to the Existence of Solutions for a Coupled System of Fractional Differential‐Integral Equations with Infinite Points and Riemann–Stieltjes Integral Boundary Conditions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    7. Youzheng Ding & Jiafa Xu & Zhengqing Fu, 2019. "Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann–Liouville Type Involving Semipositone Nonlinearities," Mathematics, MDPI, vol. 7(10), pages 1-19, October.
    8. Longfei Lin & Yansheng Liu & Daliang Zhao, 2021. "Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    9. Fang Wang & Lishan Liu & Yonghong Wu & Yumei Zou, 2019. "Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p -Laplacian Operator," Complexity, Hindawi, vol. 2019, pages 1-21, October.
    10. Yongyi Gu & Fanning Meng, 2019. "Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods," Complexity, Hindawi, vol. 2019, pages 1-11, August.
    11. Yang Yang & Jian-ming Qi & Xue-hua Tang & Yong-yi Gu, 2019. "Further Results about Traveling Wave Exact Solutions of the (2+1)‐Dimensional Modified KdV Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    12. Wanassi, Om Kalthoum & Torres, Delfim F.M., 2023. "An integral boundary fractional model to the world population growth," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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