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Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations |
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| Authors: | Ravi P. Agarwal Donal O'Regan |
| Affiliation: | a Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA b KFUPM Chair Professor, Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia c Department of Mathematics, National University of Ireland, Galway, Ireland d Department of Mathematical Analysis, Faculty of Science, Palacký University, T?. 17. listopadu 12, 771 46 Olomouc, Czech Republic |
| Abstract: | In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: Dαu(t)+f(t,u(t),Dμu(t))=0, u(0)=u(1)=0, where 1<α<2, 0<μ?α−1, Dα is the standard Riemann-Liouville fractional derivative, f is a positive Carathéodory function and f(t,x,y) is singular at x=0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques. |
| Keywords: | Fractional differential equation Singular Dirichlet problem Positive solution Riemann-Liouville fractional derivative |
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