Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives

By Xiaoqian Liu, Lishan Liu, Yonghong Wu. Boundary Value Problems, 2018

46 citations recorded by the source corpus.

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional derivatives are considered under some appropriate conditions, and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable and it includes fractional derivatives. The existence of positive solutions for boundary conditions involving fractional derivatives is established. Finally, an example is given to demonstrate the validity of our main results.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e7290610ccf4d1cadd096e6bf83fa79c73507b20

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

STABILITY RESULTS AND EXISTENCE THEOREMS FOR NONLINEAR DELAY-FRACTIONAL DIFFERENTIAL EQUATIONS WITH $ \varphi^*_P $-OPERATOR (2020, methodology): “[31] investigated EUS for a class of singular fractional DEs using index theory.”
Stability and existence results for a class of nonlinear fractional differential equations with singularity (2018, background): “By using (28), we find the operator ∗ is uniformly bounded.”