SOLVABILITY OF THE CAPUTO FRACTIONAL DIFFERENTIAL SYSTEM WITH RIEMANN-STIELTJES BOUNDARY CONDITIONS

Ying Wang; Limin Guo

doi:10.11948/20250114

2026 Volume 16 Issue 1

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(1): 34-44

Next Article Previous Article

Ying Wang, Limin Guo. SOLVABILITY OF THE CAPUTO FRACTIONAL DIFFERENTIAL SYSTEM WITH RIEMANN-STIELTJES BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 34-44. doi: 10.11948/20250114

Citation:

Ying Wang, Limin Guo. SOLVABILITY OF THE CAPUTO FRACTIONAL DIFFERENTIAL SYSTEM WITH RIEMANN-STIELTJES BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 34-44. doi: 10.11948/20250114

SOLVABILITY OF THE CAPUTO FRACTIONAL DIFFERENTIAL SYSTEM WITH RIEMANN-STIELTJES BOUNDARY CONDITIONS

Ying Wang^1, ,,
Limin Guo^2,

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

Author Bio: Email: guolimin811113@163.com(L. Guo)
Corresponding author: Email: lywy1981@163.com(Y. Wang)

Abstract

Abstract

Fractional derivative is nonlocal which exhibit a long-term memory behavior. Having these advantages, fractional order systems are more accurate than integer order ones. In this article, our research focuses on the Caputo fractional differential system with Riemann-Stieltjes integral boundary conditions. Firstly, we convert the system to an integral operator. And then, based on the properties of the Green function, we have separately proven the existence of the unique solution and at least one solution for the system by applying the Banach contraction principle and the Leray-Schauder's alternative. Finally, The correctness of the results is verified through an example.
- Solvability /
- uniqueness /
- existence /
- Caputo fractional differential system /
- Riemann-Stieltjes boundary conditions
MSC: 34B16, 34B18

FullText(HTML)

References

[1]	A. A. M. Arafa, S. Z. Rida and M. Khalil, The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional order model, Appl. Math. Modell., 2013, 37, 2189–2196. Google Scholar
[2]	A. Cabada, S. Dimitrijevic, T. Tomovic and S. Aleksic, The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions, Math. Method. Appl. Sci., 2017, 40(6), 1880–1891. Google Scholar
[3]	Y. Chen and H. Li, Existence of positive solutions for a system of nonlinear Caputo type fractional differential equations with two parameters, Adv. Dffer. Equ., 2021, 497. DOI: 10.1186/s13662-021-03650-z. CrossRef Google Scholar
[4]	A. Grans and J. Dugundji, Fixed Point Theorems, Springer, New York, 2005. Google Scholar
[5]	L. Guo, L. Liu and Y. Wu, Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters, Nonlinear Analy-Model., 2018, 23(2), 182–203. Google Scholar
[6]	L. Guo, Y. Wang, C. Li, J. Cai and B. Zhang, Solvability for a higher-order Hadanard fractional differential model with a sign-changing nonlinearlity dependent on the parameter ϱ, J. Appl. Anal. Comput., 2024, 14(5), 2762–2776. Google Scholar
[7]	H. Li and Y. Chen, Multiple positive solutions for a system of nonlinear Caputo-type fractional differential equations, J. Funct. Spaces., 2020. DOI: 10.1155/2018/2176809. CrossRef Google Scholar
[8]	W. Ma and Y. Cui, The eigenvalue problem for Caputo type fractional differential equation with Riemann-Stieltjes integral boundary conditions, J. Funct. Spaces., 2018. DOI: 10.1155/2018/2176809. CrossRef Google Scholar
[9]	K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley, New York, 1993. Google Scholar
[10]	I. Podlubny, Fractional Differential Equations. Mathematics in Science and Engineering, Vol. 198, New York/London/Toronto, Academic Press, 1999. Google Scholar
[11]	S. Shi, Z. Fu and S. Lu, On the compactness of commutators of Hardy operators, Pac. J. Math., 2020, 307, 239–256. Google Scholar
[12]	S. Shi, Z. Zhai and L. Zhang, Characterizations of the viscosity solution of a nonlocal and nonlinear equation induced by the fractional p-Laplace and the fractional p-convexity, Adv. Calc. Var., 2024, 17, 195–207. Google Scholar
[13]	Y. Wang, L. Guo, Y. Zi and J. Li, Solvability of fractional differential system with parameters and singular nonlinear terms, AIMS Mathematics, 2024, 9(8), 22435–22453. Google Scholar
[14]	Y. Wang and L. Liu, Uniqueness and existence of positive solutions for the fractional integro-differential equation, Bound. Value Probl., 2017. DOI: 10.1186/s13661-016-0741-1. CrossRef Google Scholar
[15]	Y. Wang and J. Zhang, Positive solutions for higher-order singular fractional differential system with coupled integral boundary conditions, Adv. Differ. Equ., 2016. DOI: 10.1186/s13662-016-0844-0. CrossRef Google Scholar
[16]	Q. Wu and Z. Fu, Boundedness of Hausdorff operators on Hardy spaces in the Heisen-berg group, Banach J. Math. Anal., 2018, 12, 909–934. Google Scholar
[17]	X. Zhang, P. Chen, H. Tian and Y. Wu, The iterative properties for positive solutions of a tempered fractional equation, Fractal Fract., 2023. DOI: 10.3390/fractalfract7100761. CrossRef Google Scholar
[18]	X. Zhang, P. Xu and Y. Wu, The eigenvalue problem of a singular k-Hessian equation, Appl. Math. Lett., 2022. DOI: 10.1016/j.aml.2021.107666. CrossRef Google Scholar
[19]	X. Zhang, P. Xu, Y. Wu and B. Wiwatanapataphe, The uniqueness and iterative properties of solutions for a general Hadamard-type singular fractional turbulent flow model, Nonlinear Anal. Model. Control., 2022, 27, 428–444. Google Scholar