Existence and Nonexistence of Positive Solutions for a System of Nonlinear Singular Fractional Differential Equations
نویسندگان
چکیده
In this paper, we establish sufficient conditions for the existence and nonexistence of positive solutions to the following nonlinear fractional differential system ⎪⎪⎨ ⎪⎪⎩ Dαu(t)+a(t) f (t,u,v) = 0 in (0,1) , Dβ v(t)+b(t)g(t,u,v) = 0 in (0,1) , u(0) = 0, u(1) = 0, u′(0) = 0, v(0) = 0, v(1) = 0, v′(0) = 0, (P) where 2 < α ,β 3 , a,b ∈ C ((0,1) , [0,+∞)) and the functions f ,g belong to C ([0,1]× [0,+∞) × [0,+∞) , [0,+∞)) and satisfy some appropriate conditions. Our analysis relies on Krasnoselskii fixed point theorem. Some examples are given to illustrate our results.
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