Mild solutions for fractional differential equations with nonlocal conditions.
Li, Fang (2010)
Advances in Difference Equations [electronic only]
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Li, Fang (2010)
Advances in Difference Equations [electronic only]
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Anguraj, A., Karthikeyan, P., Trujillo, J.J. (2011)
Advances in Difference Equations [electronic only]
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Lv, Zhi-Wei (2011)
Advances in Difference Equations [electronic only]
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Lv, Zhi-Wei, Liang, Jin, Xiao, Ti-Jun (2010)
Advances in Difference Equations [electronic only]
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Agarwal, Ravi P., Belmekki, Mohammed, Benchohra, Mouffak (2009)
Advances in Difference Equations [electronic only]
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Diagana, T., Mophou, G.M., N'guérékata, G.M. (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Tian, Yuansheng, Chen, Anping (2009)
Abstract and Applied Analysis
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Bai, Chuanzhi (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Ahmad, Bashir, Ntouyas, Sotiris K., Alsaedi, Ahmed (2011)
Advances in Difference Equations [electronic only]
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Belmekki, Mohammed, Nieto, Juan J., Rodríguez-López, Rosana (2009)
Boundary Value Problems [electronic only]
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Wang, Jinhua, Xiang, Hongjun, Liu, Zhigang (2010)
International Journal of Differential Equations
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Li, Fang, Zhang, Jun (2011)
Advances in Difference Equations [electronic only]
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Svatoslav Staněk (2013)
Open Mathematics
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We investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their...