Solvability of fractional differential system with parameters and singular nonlinear terms

Ying Wang; Limin Guo; Yumei Zi; Jing Li; Ying Wang; Limin Guo; Yumei Zi; Jing Li

doi:10.3934/math.20241091

AIMS Mathematics

2024, Volume 9, Issue 8: 22435-22453. doi: 10.3934/math.20241091

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Research article

Solvability of fractional differential system with parameters and singular nonlinear terms

1.
School of Mathematics and Statistics, Linyi University, Linyi 276000, Shandong, China
2.
School of Science, Changzhou Institute of Technology, Changzhou 213002, Jiangsu, China

Received: 19 April 2024 Revised: 17 June 2024 Accepted: 15 July 2024 Published: 18 July 2024
MSC : 26A33, 34B16, 34B18

In this article, we consider the parametric high-order fractional system with integral boundary value conditions involving derivatives of order $ p $-$ q $. With the aid of the fixed-point theorem, an exact interval from the existence to the solution of the system will be obtained, under the condition that the nonlinearities of the system may have singularities. Finally, we provide an instance to show the practicality of the primary outcomes.
- positive solution,
- parameter,
- fractional differential system,
- singular
Citation: Ying Wang, Limin Guo, Yumei Zi, Jing Li. Solvability of fractional differential system with parameters and singular nonlinear terms[J]. AIMS Mathematics, 2024, 9(8): 22435-22453. doi: 10.3934/math.20241091

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Abstract

In this article, we consider the parametric high-order fractional system with integral boundary value conditions involving derivatives of order $ p $-$ q $. With the aid of the fixed-point theorem, an exact interval from the existence to the solution of the system will be obtained, under the condition that the nonlinearities of the system may have singularities. Finally, we provide an instance to show the practicality of the primary outcomes.

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