EXISTENCE AND STABILITY OF SOLUTIONS FOR A COUPLED HADAMARD TYPE SEQUENCE FRACTIONAL DIFFERENTIAL SYSTEM ON GLUCOSE GRAPHS

Junping Nan; Weimin Hu; You-Hui Su; Yongzhen Yun

doi:10.11948/20230202

2024 Volume 14 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(2): 911-946

Next Article Previous Article

Junping Nan, Weimin Hu, You-Hui Su, Yongzhen Yun. EXISTENCE AND STABILITY OF SOLUTIONS FOR A COUPLED HADAMARD TYPE SEQUENCE FRACTIONAL DIFFERENTIAL SYSTEM ON GLUCOSE GRAPHS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 911-946. doi: 10.11948/20230202

Citation:

Junping Nan, Weimin Hu, You-Hui Su, Yongzhen Yun. EXISTENCE AND STABILITY OF SOLUTIONS FOR A COUPLED HADAMARD TYPE SEQUENCE FRACTIONAL DIFFERENTIAL SYSTEM ON GLUCOSE GRAPHS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 911-946. doi: 10.11948/20230202

EXISTENCE AND STABILITY OF SOLUTIONS FOR A COUPLED HADAMARD TYPE SEQUENCE FRACTIONAL DIFFERENTIAL SYSTEM ON GLUCOSE GRAPHS

1.
School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, Jiangsu, China
2.
School of Mathematics and Statistics, Yili Normal University, Yining 839300, Xinjiang, China
3.
Institute of Applied Mathematic, Yili Normal University, Yining 839300, Xinjiang, China

Author Bio: Email: njp7928@sina.com(J. Nan); Email: yunyz@xzit.edu.cn(Y. Yun)
Corresponding authors: Email: Hwm680702@163.com(W. Hu); Email: suyh02@163.com(Y. Su)
Fund Project: This work is supported by the the Xuzhou Science and Technology Plan Project (No. KC23058) and the Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2023D01C51)

Abstract

Abstract

Chemical graph theory is an interdisciplinary mathematics and chemistry discipline that obtains mathematical information about the structure of target compounds and is an important research branch in theoretical pharmacology and nanomedicine. This paper study a coupled Hadamard type sequential fractional differential system on glucose graphs and establishes the Ulam's stability and existence of the system solutions. Furthermore, we examine examples against different background graphs and provide approximate graphs of the solutions. The novelty of this paper is that the origin of each edge is not fixed in modeling the glucose graphs, and one of the two vertices of the corresponding edge can be arbitrarily chosen as the origin to build the system and give the approximate graphs of the solutions using iterative methods and numerical simulation.
- Chemical graph theory /
- fractional differential system /
- glucose graphs /
- Ulam's stability /
- numerical simulation
MSC: 34A08, 34B15, 34B45

FullText(HTML)

References

[1]	A. Z. Abdian, A. Behmaram and G. H. Fath-Tabar, Graphs determined by signless Laplacian spectra, Akce. Int. J. Graphs. Co., 2020, 17(1), 45-50. doi: 10.1016/j.akcej.2018.06.009 CrossRef Google Scholar
[2]	B. Ahmad, M. Alghanmi, A. Alsaedi, et al., Existence and uniqueness results for a nonlinear coupled system involving Caputo fractional derivatives with a new kind of coupled boundary conditions, Appl. Math. Lett., 2021, 116, 107018. doi: 10.1016/j.aml.2021.107018 CrossRef Google Scholar
[3]	B. Ahmad, A. Alsaedi, S. K. Ntouyas, et al., Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, Cham, Switzerland, Springer, 2017. Google Scholar
[4]	A. Boroomand and M. B. Menhaj, Fractional-order hopfeld neural networks, Lect. Notes. Comput. Sc., 2009, 5509, 883-890. Google Scholar
[5]	L. Debnath, Fractional integrals and fractional differential equations in fluid mechanics, Frac. Calc. Appl. Anal., 2003, 6, 119155. Google Scholar
[6]	A. Din, Y. J. Li and A. Yusuf, Delayed hepatitis B epidemic model with stochastic analysis, Chao. Soliton. Fract., 2021, 146(1), 110839. Google Scholar
[7]	R. George, M. Houas, M. Ghaderi, et al., On a coupled system of pantograph problem with three sequential fractional derivatives by using positive contraction-type inequalities, Results Phys., 2022, 39, 105687. doi: 10.1016/j.rinp.2022.105687 CrossRef Google Scholar
[8]	B. Ghanbari, On approximate solutions for a fractional prey-predator model involving the Atangana-Baleanu derivative, Adv. Differ. Equ-Ny., 2020, 1, 679. Google Scholar
[9]	D. G. Gordeziani, M. Kupreishvli, H. V. Meladze, et al., On the solution of boundary value problem for differential equations given in graphs, Appl. Math. Lett., 2008, 13, 80-91. Google Scholar
[10]	J. R. Graef, L. J. Kong and M. Wang, Existence and uniqueness of solutions for a fractional boundary value problem on a graph, Fract. Calc. Appl. Anal., 2014, 17, 499-510. doi: 10.2478/s13540-014-0182-4 CrossRef Google Scholar
[11]	Z. J. Han and E. Zuazua, Decay rates for elastic-thermoelastic star-shaped networks, Netw. Heterog. Media., 2017, 12(3), 461-488. doi: 10.3934/nhm.2017020 CrossRef Google Scholar
[12]	A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam, Elsevier, 2006. Google Scholar
[13]	J. Klafter, S. C. Lim and R. Metzler, Fractional Dynamics in Physics, Singapore, World Scientific, 2011. Google Scholar
[14]	M. A. Krasnoselskii, Two remarks on the method of successive approximations, Uspekhi. Mat. Nauk., 1955, 10, 123-127. Google Scholar
[15]	C. S. Liu, E. R. El-Zahar and C. W. Chang, A boundary shape function iterative method for solving nonlinear singular boundary value problems, Math. Comput. Simul., 2021, 187, 614-629. doi: 10.1016/j.matcom.2021.03.030 CrossRef Google Scholar
[16]	G. Lumer, Connecting of local operators and evolution equations on a network, Lect. Notes. Math., 1980, 787, 219-234. Google Scholar
[17]	A. Mahdy, M. S. Mohamed, K. A. Gepreel, et al., Dynamical characteristics and signal flow graph of nonlinear fractional smoking mathematical model, Chaos Soliton. Fract., 2020, 141, 110308. doi: 10.1016/j.chaos.2020.110308 CrossRef Google Scholar
[18]	V. Mehandiratta, M. Mehra and G. Leugering, Existence and uniqueness results for a nonlinear Caputo fractional boundary value problem on a star graphs, J. Math. Anal. Appl., 2019, 477(2), 1243-1264. doi: 10.1016/j.jmaa.2019.05.011 CrossRef Google Scholar
[19]	R. Metzler and J. Klafter, Boundary value problems for fractional diffusion equations, Phys A., 2000, 278(1-2), 107-125. doi: 10.1016/S0378-4371(99)00503-8 CrossRef Google Scholar
[20]	S. Nicaise, Some results on spectral theory over networks applied to nerve impulse transmission, Lect. Notes. Math., 1985, 1771, 532-541. Google Scholar
[21]	V. Pivovarchik, Inverse problem for the Sturm-Liouville equation on a star-shaped graph, Math. Nachr., 2007, 280(13), 1595-1619. Google Scholar
[22]	M. Ruziev, A boundary value problem for a partial differential equation with fractional derivative, Fract. Cacl. Appl., 2021, 24(2), 509-517. doi: 10.1515/fca-2021-0022 CrossRef Google Scholar
[23]	D. L. Shah and M. Alam, Hyers-Ulam stability of coupled implicit fractional integro-differential equations with Riemann-Liouville derivatives, Chaos. Soliton. Fract., 2021, 150, 111122. doi: 10.1016/j.chaos.2021.111122 CrossRef Google Scholar
[24]	N. A. Sheikh, M. Jamil, D. Ching, et al., A generalized model for quantitative analysis of sediments loss: A Caputo time fractional model, J. King Saud. Univ. Sci., 2020, 33(1), 101179. Google Scholar
[25]	R. Subashini, K. Jothimani, K. S. Nisar, et al., New results on nonlocal functional integro-differential equations via Hilfer fractional derivative, Alex. Eng. J., 2020, 59(5), 2891-2899. doi: 10.1016/j.aej.2020.01.055 CrossRef Google Scholar
[26]	A. N. Sultan, Nonlinear convolution integro-differential equation with variable coefficient, Fract. Cacl. Appl., 2021, 24(3), 848-864. doi: 10.1515/fca-2021-0036 CrossRef Google Scholar
[27]	A. Sun, Y. H. Su and J. P. Sun, Existence of solutions to a class of fractional differential equations, J. Nonlinear. Model. Anal., 2022, 4, 409-442. Google Scholar
[28]	A. Sun, Y. H. Su, Q. C. Yuan, et. al., Existence of solutions to fractional differential equations with fractional-order derivative terms, J. Appl. Anal. Comput., 2021, 11, 486-520. Google Scholar
[29]	W. C. Sun, Y. H. Su and X. L. Han, Existence of solutions for a coupled system of caputo-hadamard fractional differential equations with p-laplacian operator, J. Appl. Anal. Comput, 2022, 12, 1885-1900. Google Scholar
[30]	W. C. Sun, Y. H. Su, A. Sun, et. al., Existence and simulation of positive solutions for m-point fractional differential equations with derivative terms, Open. Math., 2021, 19, 1820-1846. doi: 10.1515/math-2021-0131 CrossRef Google Scholar
[31]	J. Tariboon, S. K. Ntouyas, S. Asawasamrit, et al., Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain, Open Math., 2017, 15(1), 645-666. doi: 10.1515/math-2017-0057 CrossRef Google Scholar
[32]	D. Tripathil, S. Pandey and S. Das, Peristaltic flow of viscoelastic fluid with fractional maxwell model through a channel, Appl. Math. Comput., 2010, 215, 3645-3654. Google Scholar
[33]	A. Turab and W. Sintunavarat, The novel existence results of solutions for a nonlinear fractional boundary value problem on the ethane graph, Alex. Eng. J., 2021, 60(6), 5365-5374. doi: 10.1016/j.aej.2021.04.020 CrossRef Google Scholar
[34]	J. R. Wang, Y. Zhou and M. Medve, Existence and stability of fractional differential equations with Hadamard derivative, Topol. Method Nonl. An., 2013, 41(1), 113-133. Google Scholar
[35]	S. H. Wang and Z. Zhou, Three solutions for a partial discrete Dirichlet boundary value problem with p-Laplacian, Bound. Value. Probl., 2021, 2021(1), 39. doi: 10.1186/s13661-021-01514-9 CrossRef Google Scholar
[36]	T. Yu, L. Zhang, Y. D. Ji, et al., Stochastic resonance of two coupled fractional harmonic oscillators with fluctuating mass, Commun. Nonlinear. Sci., 2019, 72, 26-38. doi: 10.1016/j.cnsns.2018.11.009 CrossRef Google Scholar
[37]	M. G. Zavgorodnii and Y. V. Pokornyi, On the spectrum of second-order boundary value problems on spatial networks, Usp. Mat. Nauk., 1989, 44, 220-221. Google Scholar
[38]	B. L. Zhang, V. D. Rdulescu and L. Wang, Existence results for Kirchhoff-type superlinear problems involving the fractional Laplacian, P. Roy. Soc. Edinb. A., 2018, 149(4), 1061-1081. Google Scholar
[39]	H. Y. Zhang, J. J. Ao and D. Mu, Eigenvalues of discontinuous third-order boundary value problems with eigenparameter-dependent boundary conditions, J. Math. Anal. Appl., 2021, 506(2), 125680. Google Scholar
[40]	W. Zhang and W. Liu, Existence and Ulam's type stability results for a class of fractional boundary value problems on a star graphs, Math. Method Appl. Sci., 2020, 43, 8568-8594. doi: 10.1002/mma.6516 CrossRef Google Scholar