Multiple positive solutions for nonlinear singular Katugampola fractional differential equations with nonlocal coupled Riemann-Stieltjes integral boundary conditions

Wengui Yang; Wengui Yang

doi:10.3934/era.2026024

Electronic Research Archive

2026, Volume 34, Issue 1: 509-533. doi: 10.3934/era.2026024

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Research article

Multiple positive solutions for nonlinear singular Katugampola fractional differential equations with nonlocal coupled Riemann-Stieltjes integral boundary conditions

Wengui Yang ^,

School of Education and Humanities, Sanmenxia Polytechnic, Sanmenxia 472000, China

Received: 23 September 2025 Revised: 02 January 2026 Accepted: 12 January 2026 Published: 16 January 2026

This study explores a system of singular nonlinear higher-order katugampola fractional differential equations (KFDEs) with nonlocal coupled Riemann-Stieltjes integral boundary conditions. First, the addressed KFDEs are reformulated as the equivalent integral equations through explicit construction of some appropriate Green's functions. Second, through synergistic application of Schauder's and Guo-Krasnoselskii's fixed-point theorems, some explicit parameter interval-dependent existence criteria are established for at least one or two positive solutions to the considered KFDEs with the help of the properties of Green's functions. Finally, some concrete examples are provided to validate the effectiveness of the main theoretical results.
Citation: Wengui Yang. Multiple positive solutions for nonlinear singular Katugampola fractional differential equations with nonlocal coupled Riemann-Stieltjes integral boundary conditions[J]. Electronic Research Archive, 2026, 34(1): 509-533. doi: 10.3934/era.2026024

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Abstract

This study explores a system of singular nonlinear higher-order katugampola fractional differential equations (KFDEs) with nonlocal coupled Riemann-Stieltjes integral boundary conditions. First, the addressed KFDEs are reformulated as the equivalent integral equations through explicit construction of some appropriate Green's functions. Second, through synergistic application of Schauder's and Guo-Krasnoselskii's fixed-point theorems, some explicit parameter interval-dependent existence criteria are established for at least one or two positive solutions to the considered KFDEs with the help of the properties of Green's functions. Finally, some concrete examples are provided to validate the effectiveness of the main theoretical results.

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