Existence of solutions for Hadamard fractional nonlocal boundary value problems with mean curvature operator at resonance

Teng-Fei Shen; Jian-Gen Liu; Xiao-Hui Shen; Teng-Fei Shen; Jian-Gen Liu; Xiao-Hui Shen

doi:10.3934/math.20241402

AIMS Mathematics

2024, Volume 9, Issue 10: 28895-28905. doi: 10.3934/math.20241402

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Research article

Existence of solutions for Hadamard fractional nonlocal boundary value problems with mean curvature operator at resonance

1.
School of Mathematics and Statistics, Huaibei Normal University, Huaibei 235000, Anhui, China
2.
School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, Jiangsu, China
3.
Qin Institute of Mathematics, Shanghai Hanjing Centre for Science and Technology, Yexie Town, Songjiang District, Shanghai 201609, China

Received: 22 July 2024 Revised: 02 October 2024 Accepted: 03 October 2024 Published: 14 October 2024
MSC : 26A33, 34A08, 34B15

This paper aims to study the existence of solutions for Hadamard fractional nonlocal boundary value problems with mean curvature operator at resonance. Based on the coincidence degree theory, some new results are established. Moreover, an example is given to verify our main results.
- Hadamard fractional order differential equation,
- boundary value problem,
- coincidence degree theory
Citation: Teng-Fei Shen, Jian-Gen Liu, Xiao-Hui Shen. Existence of solutions for Hadamard fractional nonlocal boundary value problems with mean curvature operator at resonance[J]. AIMS Mathematics, 2024, 9(10): 28895-28905. doi: 10.3934/math.20241402

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Abstract

This paper aims to study the existence of solutions for Hadamard fractional nonlocal boundary value problems with mean curvature operator at resonance. Based on the coincidence degree theory, some new results are established. Moreover, an example is given to verify our main results.

References

[1]	A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Amsterdam: Elsevier, 2006.
[2]	I. Podlubny, Fractional differential equation, San Diego: Academic Press, 1999.
[3]	S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, theory and applications, Yverdon: Gordon and Breach, 1993.
[4]	Y. Zhou, Basic theory of fractional differential equations, Singapore: World Scientific, 2014. https://doi.org/10.1142/9069
[5]	B. Ahmad, S. K. Ntouyas, Initial-value problems for hybrid Hadamard fractional differential equations, Electron. J. Differ. Eq., 2014 (2014), 1–8. Available from: http://ejde.math.txstate.edu/.
[6]	B. Ahmad, S. K. Ntouyas, On Hadamard fractional integro-differential boundary value problems, J. Appl. Math. Comput., 47 (2015), 119–131. http://doi.org/10.1007/s12190-014-0765-6 doi: 10.1007/s12190-014-0765-6
[7]	B. Ahmad, S. K. Ntouyas, Hilfer-Hadamard fractional boundary value problems with nonlocal mixed boundary conditions, Fractal Fract., 5 (2021), 195. https://doi.org/10.3390/fractalfract5040195 doi: 10.3390/fractalfract5040195
[8]	B. Ahmad, A. Alsaedi, S. K. Ntouyas, J. Tariboon, Hadamard-type fractional differential equations, inclusions and inequalities, Berlin: Springer, 2017. https://doi.org/10.1007/978-3-319-52141-1
[9]	K. Pei, G. T. Wang, Y. Y. Sun, Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain, Appl. Math. Comput., 312 (2017), 158–168. https://doi.org/10.1016/j.amc.2017.05.056 doi: 10.1016/j.amc.2017.05.056
[10]	W. Zhang, W. B. Liu, Existence of solutions for several higher-order Hadamard-type fractional differential equations with integral boundary conditions on infinite interval, Bound. Value Probl., 2018 (2018), 134. https://doi.org/10.1186/s13661-018-1053-4 doi: 10.1186/s13661-018-1053-4
[11]	J. Jiang, D. O'Regan, J. Xu, Y. Cui, Positive solutions for a Hadamard fractional $p$-laplacian three-point boundary value problem, Mathematics, 7 (2019), 439. https://doi.org/10.3390/math7050439 doi: 10.3390/math7050439
[12]	J. R. Wang, Y. Zhang, On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives, Appl. Math. Lett., 39 (2015), 85–90. https://doi.org/10.1016/j.aml.2014.08.015 doi: 10.1016/j.aml.2014.08.015
[13]	C. Zhai, W. Wang, H. Li, A uniqueness method to a new Hadamard fractional differential system with four-point boundary conditions, J. Inequal. Appl., 2018 (2018), 207. https://doi.org/10.1186/s13660-018-1801-0 doi: 10.1186/s13660-018-1801-0
[14]	T. Shen, Multiplicity of positive solutions to Hadamard-type fractional relativistic oscillator equation with $p$-Laplacian operator, Fractal Fract., 7 (2023), 427. https://doi.org/10.3390/fractalfract7060427 doi: 10.3390/fractalfract7060427
[15]	M. Benchohra, S. Bouriah, A. Salim, Y. Zhou, Fractional differential equations: A coincidence degree approach, Berlin, Boston: De Gruyter, 2024. https://doi.org/10.1515/9783111334387
[16]	P. L. Li, R. Gao, C. J. Xu, Y. Li, A. Akgül, D. Baleanu, Dynamics exploration for a fractional-order delayed zooplankton-phytoplankton system, Chaos Soliton. Fract., 166 (2023), 112975. https://doi.org/10.1016/j.chaos.2022.112975 doi: 10.1016/j.chaos.2022.112975
[17]	Z. H. Liu, X. W. Li, Approximate controllability of fractional evolution systems with Riemann-Liouville fractional derivatives, SIAM J. Control Optim., 53 (4) (2015), 1920–1933. https://doi.org/10.1137/1209038 doi: 10.1137/1209038
[18]	X. W. Li, Z. H. Liu, J. Li, C. Tisdell, Existence and controllability for nonlinear fractional control systems with damping in Hilbert spaces, Acta Math. Sci., 39 (1) (2019), 229–242. https://doi.org/10.1007/s10473-019-0118-5 doi: 10.1007/s10473-019-0118-5
[19]	C. Bereanu, J. Mawhin, Existence and multiplicity results for some nonlinear problems with singular $\phi$-Laplacian, J. Differ. Equations., 243 (2007), 536–557. https://doi.org/10.1016/j.jde.2007.05.014 doi: 10.1016/j.jde.2007.05.014
[20]	P. Jebelean, J. Mawhin, C. Şerban, Multiple periodic solutions for perturbed relativistic pendulum systems, P. Am. Math. Soc., 143 (2015), 3029–3039. https://doi.org/10.1090/S0002-9939-2015-12542-7 doi: 10.1090/S0002-9939-2015-12542-7
[21]	D. Arcoya, C. Sportelli, Relativistic equations with singular potentials, Z. Angew. Math. Phys., 74 (2023), 91. https://doi.org/10.1007/s00033-023-01977-z doi: 10.1007/s00033-023-01977-z
[22]	C. Alves, C. T. Ledesma, Multiplicity of solution for some slasses of prescribed mean curvature equation with Dirichlet boundary condition, J. Geom. Anal., 32 (2022), 262. https://doi.org/10.1007/s12220-022-01010-1 doi: 10.1007/s12220-022-01010-1
[23]	C. T. Ledesma, Multiplicity of solutions for some classes of prescribed mean curvature equations with local conditions, Mediterr. J. Math., 20 (2023), 215. https://doi.org/10.1007/s00009-023-02418-x doi: 10.1007/s00009-023-02418-x
[24]	J. Mawhin, Topological degree and boundary value problems for nonlinear differential equations in topological methods for ordinary differential equations, Lect. Notes Math., 1537 (1993), 74–142. https://doi.org/10.1007/BFb0085076 doi: 10.1007/BFb0085076

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