Existence of positive solutions for singular higher-order fractional differential equation via spectral analysis. (English) Zbl 1377.34011
Summary: In this paper, the existence of positive solutions for a class of fractional differential equations with Riemann-Stieltjes integral boundary conditions are investigated under some weak conditions concerning the spectral analysis of the relevant linear operator and Gelfand’s formula by means of the fixed point index theorem in cones. The nonlinearity permits singularities not only at \(t=0,1\), but also at \(x_{i}=0\) (\(i=1,2,\dots,n-1\)). The results obtained herein generalize and improve some known results including singular and non-singular cases.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B16 | Singular nonlinear boundary value problems for ordinary differential equations |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
fractional differential equation; positive solution; singularity; fixed point index; spectral analysisReferences:
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