Abstract
In this paper, we consider the following two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions for the following boundary value problems that the nonlinear terms contain i-order derivative
where n−1<α≤n is a real number, n is natural number and n≥2, α−i>1, i∈N and 0≤i≤n−1. \({}^{c}D_{0^{+}}^{\alpha}\) is the standard Caputo derivative. f(t,x 0,x 1,…,x i ) may be singular at t=0.
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The authors would like to thank the referee for his/her valuable comments and suggestions.
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The project is supported financially by the Foundation for Outstanding Middle-Aged and Young Scientists of Shandong Province (BS2010SF004), the National Natural Science Foundation of China (10971179), and a Project of Shandong Province Higher Educational Science and Technology Program (No. J10LA53).
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Guo, L., Zhang, X. Existence of positive solutions for the singular fractional differential equations. J. Appl. Math. Comput. 44, 215–228 (2014). https://doi.org/10.1007/s12190-013-0689-6
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DOI: https://doi.org/10.1007/s12190-013-0689-6
Keywords
- Fractional differential equation
- Positive solution
- Fractional Green’s function
- Avery-Peterson fixed point theorem