THE METHOD OF LOWER AND UPPER SOLUTIONS FOR FRACTIONAL DIFFERENTIAL SYSTEM WITH <i>P</i>-LAPLACIAN OPERATORS

Lina Guo; Chengmin Hou; Mingzhe Sun

doi:10.11948/20240584

2026 Volume 16 Issue 1

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(1): 121-135

Next Article Previous Article

Lina Guo, Chengmin Hou, Mingzhe Sun. THE METHOD OF LOWER AND UPPER SOLUTIONS FOR FRACTIONAL DIFFERENTIAL SYSTEM WITH P-LAPLACIAN OPERATORS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 121-135. doi: 10.11948/20240584

Citation:

Lina Guo, Chengmin Hou, Mingzhe Sun. THE METHOD OF LOWER AND UPPER SOLUTIONS FOR FRACTIONAL DIFFERENTIAL SYSTEM WITH P-LAPLACIAN OPERATORS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 121-135. doi: 10.11948/20240584

THE METHOD OF LOWER AND UPPER SOLUTIONS FOR FRACTIONAL DIFFERENTIAL SYSTEM WITH P-LAPLACIAN OPERATORS

1.
Department of Mathematics and Physics, Yantai Nanshan University, Longkou 265713, China
2.
Department of Basic Teaching, Xinjiang University of Political Science and Law, Tumshuq 843806, China
3.
Department of Mathematics, Yanbian University, Yanji 133002, China

Author Bio: Email: 158722492@qq.com(L. Guo); Email: cmhou@foxmail.com(C. Hou)
Corresponding author: Email: 35841110@qq.com(M. Sun)
Fund Project: The authors were supported by the the Science and Technology Development Plan Project of Jilin Province (20230101290JC), the Science and Technology Research Project of Jilin Provincial Department of Education (JJKH20250394KJ) and Yanbian University Ph.D. Startup Research Fund Project (ydbq202401)

Abstract

Abstract

This paper focuses on the multi-point boundary value problem for a nonlinear fractional differential system, involving p-Laplacian operator and integral boundary conditions, which arises from many complex processes such as the nonlinear phenomena in nonNewtonian fluids and mathematical modeling. Based on the monotone iterative technique, a new method of lower and upper solutions are proposed. Some new results on the existence of positive solutions for multi-point boundary value problem with integral boundary conditions are established. Finally, an example is presented to illustrate the wide range of potential applications of our main results.
- Fractional differential system /
- p-Laplacian operators /
- lower and upper solutions
MSC: 26A33,34B155

FullText(HTML)

References

[1]	M. Azouzi and L. Guedda, Existence result for nonlocal boundary value problem of fractional order at resonance with p-Laplacian operator, Azerbaijan Journal of Mathematics, 2023, 13. Google Scholar
[2]	C. Bai, Existence and uniqueness of solutions for fractional boundary value problems with p-Laplacian operator, Adv. Differential Equations, 2018, 4(2018). DOI: 10.1186/s13662-017-1460-3. CrossRef Google Scholar
[3]	F. Chabane, S. Abbas, M. Benbachir, et al., Existence of concave positive solutions for nonlinear fractional differential equation with p-Laplacian operator, Vietnam Journal of Mathematics, 2023, 51, 505-543. DOI: 10.1007/s10013-022-00552-9. CrossRef Google Scholar
[4]	L. Guo, C. Li, N. Qiao and J. Zhao, Convergence analysis of positive solution for Caputo-Hadamard fractional differential equation, Nonlinear Analysis: Modelling and Control, 2025, 1-19. Google Scholar
[5]	L. Guo and L. Liu, Maximal and minimal iterative positive solutions for singular infinite-point p-Laplacian fractional differential equations, Nonlinear Anal. Model. Control, 2018, 23(6), 851-865. Google Scholar
[6]	L. Guo, L. Liu and Y. Wu, Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters, Nonlinear Anal. Model. Control, 2018, 23(2), 182-203. Google Scholar
[7]	L. Guo, Y. Wang and C. Li, Solvability for a higher-order Hadamard fractional differential model with a sign-changing nonlinearity dependent on the parameter, Journal of Applied Analysis Computation, 2024, 14, 2762-2776. Google Scholar
[8]	L. Guo, Y. Wang and H. Liu, On iterative positive solutions for a class of singular infinite-point p-Laplacian fractional differential equation with singular source terms, Journal of Applied Analysis Computation, 2023, 13(5), 2827-2842. Google Scholar
[9]	L. Guo, J. Zhao, S. Dong and X. Hou, Existence of multiple positive solutions for Caputo fractional differential equation with infinite-point boundary value conditions, Journal of Applied Analysis and Computation, 2022, 12(5), 1786-1800. DOI: 10.11948/20210301. CrossRef Google Scholar
[10]	L. Guo, J. Zhao, L. Liao and L. Liu, Existence of multiple positive solutions for a class of infinite-point singular p-Laplacian fractional differential equation with singular source terms, Nonlinear Anal. : Model. Control, 2022, 27(4), 609-629. Google Scholar
[11]	Z. Han, H. Lu and C. Zhang, Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian, Appl. Math. Comput., 2015, 257, 526-536. Google Scholar
[12]	X. Hao, H. Wang, L. Liu and Y. Cui, Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator, Boundary Value Problem, 2017, 182. DOI: 10.1186/s13661-017-0915-5. CrossRef Google Scholar
[13]	H. Jafari, D. Baleanu and H. Khan, Existence criterion for the solutions of fractional order p-Laplacian boundary value problems, Boundary Value Problem, 2015, 164, 1-10. Google Scholar
[14]	S. Li, X. Zhang, Y. Wu and L. Caccetta, Extremal solutions for p-Laplacian differential systems via iterative computation, Applied Mathematics Letters, 2013, 26, 1151-1158. Google Scholar
[15]	X. Liu, M. Jia and W. Ge, The method of lower and upper solutions for mixed fractional four-point boundary value problem with p-Laplacian operator, Applied Mathematics Letters, 2017, 65, 56-62. Google Scholar
[16]	X. Liu, M. Jia and X. Xiang, On the solvability of a fractional differential equation model involving the p-Laplacian operator, Comput. Math. Appl., 2012, 64, 3267-3275. Google Scholar
[17]	Y. Liu and X. Yang, Resonant boundary value problems for singular multi-term fractional differential equations, J. Differ. Equ. Appl., 2013, 5, 409-472. Google Scholar
[18]	T. Ren, S. Li, X. Zhang and L. Liu, Maximum and minimum solutions for a nonlocal p-Laplacian fractional differential system from eco-economical processes, Boundary Value Problem, 2017, 118. DOI: 10.1186/s13661-017-0849-y. CrossRef Google Scholar
[19]	S. Rezapour, M. Abbas, S. Etemad, et al., On a multi-point p-Laplacian fragmental differential equation with generalized fragment difference, Mathematical Methods in the Applied Sciences, 2023, 46(7), 8390-8407. DOI: 10.1002/mma.8301. CrossRef Google Scholar
[20]	W. Sun, Y. Su and X. Han, Existence of solutions for a coupled system of Caputo-Hadamard fractional differential equations with p-Laplacian operators, Journal of Applied Analysis and Computation, 2022, 1885-1900. DOI: 10.11948/20210384. CrossRef Google Scholar
[21]	H. Wang and J. Jiang, Existence and multiplicity of positive solutions for a system of nonlinear fractional multi-point boundary value problems with p-laplacian operator, Journal of Applied Analysis and Computation, 2021, 351-366. DOI: 10.11948/20200021. CrossRef Google Scholar
[22]	K. Wang and Q. Zhou, Multiple positive solutions for nonlinear eigenvalue problems involving p-Laplacian-Like Operators, Mediterr. J. Math., 2023, 334. DOI: 10.1007/s00009-023-02548-2. CrossRef Google Scholar
[23]	Y. Wang and J. Jiang, Existence and nonexistence of positive solutions for the fractional coupled system involving generalized p-Laplacian, Adv. Differential Equations, 2017, 337. DOI: 10.1186/s13662-017-1385-x. CrossRef Google Scholar
[24]	J. Wu, X. Zhang, L. Liu, Y. Wu and Y. Cui, The convergence analysis and error estimation for unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity, Boundary Value Problem, 2018, 82(2018). DOI: 10.1186/s13661-018-1003-1. CrossRef Google Scholar
[25]	F. Yan, M. Zuo and X. Hao, Positive solution for a fractional singular boundary value problem with p-Laplacian operator, Boundary Value Problem, 2018, 51. DOI: 10.1186/s13661-018-0972-4. CrossRef Google Scholar
[26]	X. Zhang, L. Liu, B. Wiwatanapataphee and Y. Wu, The eigenvalue for a class of singular p-Laplacian fractional differentialequations involving the Riemann-Stieltjes integral boundary condition, Appl. Math. Comput., 2014, 235, 412-422. Google Scholar