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Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative

Author

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  • Changyou Wang
  • Haiqiang Zhang
  • Shu Wang

Abstract

This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained.

Suggested Citation

  • Changyou Wang & Haiqiang Zhang & Shu Wang, 2012. "Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-16, October.
    • Handle: RePEc:hin:jnddns:425408
    DOI: 10.1155/2012/425408
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    Cited by:

    1. Guotao Wang & Abdeljabbar Ghanmi & Samah Horrigue & Samar Madian, 2019. "Existence Result and Uniqueness for Some Fractional Problem," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    2. Alberto Cabada & Lucía López-Somoza & Mouhcine Yousfi, 2021. "Green’s Function Related to a n -th Order Linear Differential Equation Coupled to Arbitrary Linear Non-Local Boundary Conditions," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    3. Jeongmi Jeong & Chan-Gyun Kim, 2020. "Existence of Positive Solutions to Singular φ -Laplacian Nonlocal Boundary Value Problems when φ is a Sup-multiplicative-like Function," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    4. Pshtiwan Othman Mohammed & José António Tenreiro Machado & Juan L. G. Guirao & Ravi P. Agarwal, 2021. "Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 9(9), pages 1-18, May.
    5. Kamal Shah & Poom Kumam & Inam Ullah, 2019. "On Ulam Stability and Multiplicity Results to a Nonlinear Coupled System with Integral Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-20, February.

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