Abstract
In this paper, we consider the existence of positive solutions for a Hadamard-type fractional differential equation with singular nonlinearity. By using the spectral construct analysis for the corresponding linear operator and calculating the fixed point index of the nonlinear operator, the criteria of the existence of positive solutions for equation considered are established. The interesting point is that the nonlinear term possesses singularity at the time and space variables.
Highlights
We focus on the existence of positive solutions for the following singular Hadamard-type fractional differential equation:
It is more difficult to obtain the qualitative properties of solutions for Hadamard-type fractional differential equations since Hadamard derivatives possess a singular logarithmic kernel [99–106]
We focus on the existence of positive solutions for the Hadamard-type fractional differential equation (1) with singularity in space variables
Summary
We focus on the existence of positive solutions for the following singular Hadamard-type fractional differential equation:. By using the fixed point index theory, Wang [69] established the existence and multiplicity of positive solutions for the following nonlocal singular fractional differential equation:. It is more difficult to obtain the qualitative properties of solutions for Hadamard-type fractional differential equations since Hadamard derivatives possess a singular logarithmic kernel [99–106]. We focus on the existence of positive solutions for the Hadamard-type fractional differential equation (1) with singularity in space variables.
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