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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 837437, 7 pages
Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations
1Department of Mathematics, Cankaya University, Ogretmenler Cad. 14 06530, Balgat, Ankara, Turkey
2Institute of Space Sciences, Magurele, Bucharest, Romania
3Department of Mathematics, Azarbaijan University of Shahid Madani, Tabriz, Iran
Received 23 January 2012; Accepted 20 March 2012
Academic Editor: Juan J. Trujillo
Copyright © 2012 D. Baleanu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. P. Agarwal, D. O'Regan Donal, and S. Staněk, “Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 371, no. 1, pp. 57–68, 2010.
- K. Balachandran, S. Kiruthika, and J. J. Trujillo, “Remark on the existence results for fractional impulsive integrodifferential equations in Banach spaces,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 6, pp. 2244–2247, 2012.
- F. Chen, J. J. Nieto, and Y. Zhou, “Global attractivity for nonlinear fractional differential equations,” Nonlinear Analysis. Real World Applications, vol. 13, no. 1, pp. 287–298, 2012.
- D. Băleanu, R. P. Agarwal, O. G. Mustafa, and M. Coşulschi, “Asymptotic integration of some nonlinear differential equations with fractional time derivative,” Journal of Physics A, vol. 44, no. 5, Article ID 055203, 2011.
- D. Băleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, Complexity, Nonlinearity and Chaos, World Scientific, 2012.
- A. A. Kilbas, O. I. Marichev, and S. G. Samko, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Application of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier, 2006.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- R. Gorenflo and F. Mainardi, “Fractional calculus: integral and differential equations of fractional order,” in Fractals and Fractional Calculus in Continuum Mechanics (Udine, 1996), vol. 378 of CISM Courses and Lectures, pp. 223–276, Springer, Vienna, Austria, 1997.
- R. Gorenflo and F. Mainardi, “Fractional relaxation of distributed order,” in Complexus Mundi, pp. 33–42, World Scientific, Hackensack, NJ, USA, 2006.
- F. Mainardi, A. Mura, G. Pagnini, and R. Gorenflo, “Sub-diffusion equations of fractional order and their fundamental solutions,” in Proceedings of the International Symposium on Mathematical Methods in Engineering, J. A. Tenreiro-Machado and D. Baleanu, Eds., pp. 23–55, Springer, Ankara, Turkey, 2006.
- F. Mainardi, Y. Luchko, and G. Pagnini, “The fundamental solution of the space-time fractional diffusion equation,” Fractional Calculus & Applied Analysis, vol. 4, no. 2, pp. 153–192, 2001.
- A. V. Chechkin, R. Gorenflo, I. M. Sokolov, and V. Yu. Gonchar, “Distributed order time fractional diffusion equation,” Fractional Calculus & Applied Analysis, vol. 6, no. 3, pp. 259–279, 2003.
- A. Kochubei, “Distributed order calculus and equations of ultraslow diffusion,” Journal of Mathematical Analysis and Applications, vol. 340, no. 1, pp. 252–281, 2008.
- K. S. Miller, “Fractional differential equations,” Journal of Fractional Calculus, vol. 3, pp. 49–57, 1993.
- V. Daftardar-Gejji and A. Babakhani, “Analysis of a system of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 511–522, 2004.
- S. Q. Zhang, “The existence of a positive solution for a nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 252, no. 2, pp. 804–812, 2000.
- S. Q. Zhang, “Existence of positive solution for some class of nonlinear fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 278, no. 1, pp. 136–148, 2003.
- Z. Bai and H. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005.
- M. Stojanović, “Existence-uniqueness result for a nonlinear n-term fractional equation,” Journal of Mathematical Analysis and Applications, vol. 353, no. 1, pp. 244–255, 2009.
- M. A. Krasnoselski, Positive Solutions of Operator Equations, P. Noordhoff, Groningen, The Netherlands, 1964.
- R. W. Leggett and L. R. Williams, “Multiple positive fixed points of nonlinear operators on ordered Banach spaces,” Indiana University Mathematics Journal, vol. 28, no. 4, pp. 673–688, 1979.