Existence of Positive Solutions to the Singular Initial Value Problems of Fractional Differential Equations

Qiu Ping Li; Shu Rong Sun; Zhen Lai Han; Yi Ge Zhao

doi:10.4028/www.scientific.net/AMR.403-408.563

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 403-408Existence of Positive Solutions to the Singular...

Existence of Positive Solutions to the Singular Initial Value Problems of Fractional Differential Equations

Abstract:

In this paper, we consider the existence of positive solutions for the initial value problem of nonlinear fractional differential equations where and is the Riemann–Liouville fractional derivative. By using the Nonlinear Alternative of Leray and Schauder theorem, some sufficient conditions for the existence of at least one positive solution for the initial value problem are established.

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Advanced Materials Research (Volumes 403-408)

Pages:

563-569

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.403-408.563

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Online since:

November 2011

Authors:

Qiu Ping Li, Shu Rong Sun, Zhen Lai Han, Yi Ge Zhao

Keywords:

Fractional Differential Equation, Initial Value Problem, Nonlinear Alternative of Leray, Positive Solutions, Schauder Theorem, Singular

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References

[1] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation. New York: John Wiley, (1993).

Google Scholar

[2] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering. New York: Academic Press, (1999).

Google Scholar

[3] S. Zhang, Existence of positive solution for a singular initial value problem for fractional differential equations, Appl. Math. Comput. 49 (2005), 73–80.

Google Scholar

[4] A. Babakhani and Varsha Daftardar-Gejji, Existence of positive solutions of nonlinear fractional differential equations, Actm Math. Sinica, Chiniese Series, 50(2007), 813-822.

DOI: 10.1016/s0022-247x(02)00716-3

Google Scholar

[5] J. Sun and Y. Zhao, Multiplicity of positive solutions of a class of nonlinear fractional differential equations, J. Math. Anal. Appl. 278 (2003), 434–442.

Google Scholar

[6] S. Zhang, Monotone iterative method for initial value problem involving Remann-Liouville fractiaonal derivatives, Nonlinear Anal. 71 (2009), 2087–(2093).

DOI: 10.1016/j.na.2009.01.043

Google Scholar

[7] X. Xu, D. Jiang and C. Yuan, Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear Anal. 71 (2009), 4676-4688.

DOI: 10.1016/j.na.2009.03.030

Google Scholar

[8] Y. Zhao and S. Sun, On the existence of positive solutions for boundary value problems of nonlinear fractional differential equations, Proceedings of the 7th Conference on Biological Dynamic System and Stability of Differential Equation, World Academic Press, May 2010, pp.682-685.

DOI: 10.1109/mesa.2010.5551999

Google Scholar