SOLVABILITY FOR A HIGHER-ORDER HADAMARD FRACTIONAL DIFFERENTIAL MODEL WITH A SIGN-CHANGING NONLINEARITY DEPENDENT ON THE PARAMETER $\varrho$

Limin Guo; Ying Wang; Cheng Li; Jianwen Cai; Bo Zhang

doi:10.11948/20230389

2024 Volume 14 Issue 5

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Limin Guo, Ying Wang, Cheng Li, Jianwen Cai, Bo Zhang. SOLVABILITY FOR A HIGHER-ORDER HADAMARD FRACTIONAL DIFFERENTIAL MODEL WITH A SIGN-CHANGING NONLINEARITY DEPENDENT ON THE PARAMETER $\varrho$[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2762-2776. doi: 10.11948/20230389

Citation:

Limin Guo, Ying Wang, Cheng Li, Jianwen Cai, Bo Zhang. SOLVABILITY FOR A HIGHER-ORDER HADAMARD FRACTIONAL DIFFERENTIAL MODEL WITH A SIGN-CHANGING NONLINEARITY DEPENDENT ON THE PARAMETER $\varrho$[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2762-2776. doi: 10.11948/20230389

SOLVABILITY FOR A HIGHER-ORDER HADAMARD FRACTIONAL DIFFERENTIAL MODEL WITH A SIGN-CHANGING NONLINEARITY DEPENDENT ON THE PARAMETER $\varrho$

1.
School of science, Changzhou Institute of Technology, Liaohe, 213002 Changzhou, China
2.
School of Mathematicacs and Statistics, Linyi University, Linyi, 276000 Shandong, China
3.
School of Automotive Engineering, Changzhou Institute of Technology, Liaohe, 213002 Changzhou, China
4.
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 611756, China

Author Bio: Email: guolm@czu.cn(L. Guo); Email: licheng@czu.cn(C. Li); Email: caijw@czu.cn(J. Cai); Email: zhangbo2008@swjtu.edu.cn(B. Zhang)
Corresponding author: Email: lywy1981@163.com(Y. Wang)
Fund Project: This research was supported by the National Natural Science Foundation of China (12271232, 12101086), the major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province(22KJA460001, 23KJA580001), Changzhou Science and Technology Plan Project (CE20235049), and Open Project of Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province (SZDKF-202102)

Abstract

Abstract

In this paper, based on the properties of the Green's function, the existence of positive solutions are obtained for a Hadamard fractional differential equation with a higher-order sign-changing nonlinearity under some conditions by the fixed point theorem, and the existence of positive solutions is dependent on the parameter $\varrho$ for the Semipositive problem.
- Semipositive problem /
- Hadamard fractional differential equation /
- positive solution /
- parameter
MSC: 34B16, 34B18

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References

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