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The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations. (English) Zbl 1221.34068

Summary: We study the existence of multiple positive solutions for the nonlinear fractional differential equation boundary value problem

D 0 + α u(t)+f(t,u(t))=0,0<t<1,u(0)=u ' (0)=u ' (1)=0,

where 2<α3 is a real number and D 0 + α is the Riemann-Liouville fractional derivative. Using the properties of the Green’s function, the lower and upper solution method and a fixed-point theorem, some new existence criteria for singular and nonsingular fractional differential equation boundary value problems are established. As applications, examples are presented to illustrate the main results.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34A08Fractional differential equations
34A37Differential equations with impulses
47N20Applications of operator theory to differential and integral equations
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