Existence of positive solutions to singular fractional differential equations with generalized Laplacian



	Existence of positive solutions to singular fractional differential equations with generalized Laplacian


	Fixed Point Theory, Volume 26, No. 1, 2025, 91-118, February 1st, 2025 DOI: 10.24193/fpt-ro.2025.1.05 Authors: Tingzhi Cheng and Xianghui Xu Abstract: In this paper, we study the boundary value problem for a singular fractional differential equation with both generalized Laplacian and positive parameter. Based on the well-known results of fixed point index on cones due to Guo-Krasnoselskii and Leggett-Williams, we establish some sufficient conditions for the existence of at least one, two and three positive solutions, respectively. Meanwhile, some corresponding examples are also presented to illustrate the main results. Key Words and Phrases: Fractional boundary value problem, generalized Laplacian, singular weight, positive solution, fixed point index. 2010 Mathematics Subject Classification: 34A08, 34B16, 34B18, 47H10. Published on-line: February 1st, 2025. Fulltext pdf Back to volume's table of contents