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Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations

Author

Listed:
  • D. Baleanu
  • H. Mohammadi
  • Sh. Rezapour

Abstract

We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem , where is the standard Riemann-Liouville differentiation and is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.

Suggested Citation

  • D. Baleanu & H. Mohammadi & Sh. Rezapour, 2012. "Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, June.
    • Handle: RePEc:hin:jnlaaa:837437
    DOI: 10.1155/2012/837437
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    Citations

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    Cited by:

    1. Jiacai Huang & Hongsheng Li & YangQuan Chen & Qinghong Xu, 2012. "Robust Position Control of PMSM Using Fractional‐Order Sliding Mode Controller," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Dumitru Baleanu & Sayyedeh Zahra Nazemi & Shahram Rezapour, 2013. "The Existence of Positive Solutions for a New Coupled System of Multiterm Singular Fractional Integrodifferential Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Dumitru Baleanu & Sayyedeh Zahra Nazemi & Shahram Rezapour, 2014. "A k‐Dimensional System of Fractional Neutral Functional Differential Equations with Bounded Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Mohammad Maleki & Ishak Hashim & Majid Tavassoli Kajani & Saeid Abbasbandy, 2012. "An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Panda, Sumati Kumari & Abdeljawad, Thabet & Ravichandran, C., 2020. "A complex valued approach to the solutions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation via fixed point method," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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