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Existence of solutions for a class of nonlinear boundary value problems on the hexasilinane graph. (English) Zbl 1494.34112


MSC:

34B45 Boundary value problems on graphs and networks for ordinary differential equations
26A33 Fractional derivatives and integrals
47N20 Applications of operator theory to differential and integral equations

References:

[1] Lumer, G., Connecting of local operators and evolution equations on a network, Lect. Notes Math., 787, 219-234 (1985) · Zbl 0437.35037 · doi:10.1007/BFb0086338
[2] Zavgorodnii, M. G.; Pokornyi, Y. V., On the spectrum of second-order boundary value problems on spatial networks, Usp. Mat. Nauk, 44, 220-221 (1989)
[3] Gordeziani, D. G.; Kupreishvli, M.; Meladze, H. V.; Davitashvili, T. D., On the solution of boundary value problem for differential equations given in graphs, Appl. Math. Lett., 13, 80-91 (2008) · Zbl 1200.65067
[4] Graef, J. R.; Kong, L. J.; Wang, M., Existence and uniqueness of solutions for a fractional boundary value problem on a graph, Fract. Calc. Appl. Anal., 17, 499-510 (2014) · Zbl 1308.34012 · doi:10.2478/s13540-014-0182-4
[5] Mehandiratta, V.; Mehra, M.; Leugering, G., Existence and uniqueness results for a nonlinear Caputo fractional boundary value problem on a star graph, J. Math. Anal. Appl., 477, 2, 1243-1264 (2019) · Zbl 1421.34005 · doi:10.1016/j.jmaa.2019.05.011
[6] Mophou, G.; Leugering, G.; Fotsing, P. S., Optimal control of a fractional Sturm-Liouville problem on a star graph, Optimization, 70, 3, 659-687 (2021) · Zbl 1466.49014 · doi:10.1080/02331934.2020.1730371
[7] Etemad, S.; Rezapour, S., On the existence of solutions for fractional boundary value problems on the ethane graph, Adv. Differ. Equ., 2020 (2020) · Zbl 1482.34020 · doi:10.1186/s13662-020-02736-4
[8] Baleanu, D.; Etemad, S.; Mohammadi, H.; Rezapour, S., A novel modeling of boundary value problems on the glucose graph, Commun. Nonlinear Sci. Numer. Simul., 100 (2021) · Zbl 1466.92244 · doi:10.1016/j.cnsns.2021.105844
[9] Turab, A.; Sintunavarat, W., The novel existence results of solutions for a nonlinear fractional boundary value problem on the ethane graph, Alex. Eng. J., 60, 6, 5365-5374 (2021) · doi:10.1016/j.aej.2021.04.020
[10] Turab, A.; Sintunavarat, W., A unique solution of the iterative boundary value problem for a second-order differential equation approached by fixed point results, Alex. Eng. J., 60, 6, 5797-5802 (2021) · doi:10.1016/j.aej.2021.04.031
[11] Lazreg, J. E.; Abbas, S.; Benchohra, M.; Karapınar, E., Impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces, Open Math., 19, 1, 363-372 (2021) · Zbl 1475.54031 · doi:10.1515/math-2021-0040
[12] Karapınar, E.; Fulga, A.; Rashid, M.; Shahid, L.; Aydi, H., Large contractions on quasi-metric spaces with an application to nonlinear fractional differential equations, Mathematics, 7, 5 (2019) · doi:10.3390/math7050444
[13] Alqahtani, B.; Aydi, H.; Karapınar, E.; Rakočević, V. A., Solution for Volterra fractional integral equations by hybrid contractions, Mathematics, 7 (2019) · doi:10.3390/math7080694
[14] Abdeljawad, T.; Agarwal, R. P.; Karapınar, E.; Kumari, P. S., Solutions of the nonlinear integral equation and fractional differential equation using the technique of a fixed point with a numerical experiment in extended b-metric space, Symmetry, 11 (2019) · Zbl 1425.47016 · doi:10.3390/sym11050686
[15] Afshari, H.; Atapour, M.; Karapinar, E., A discussion on a generalized Geraghty multi-valued mappings and applications, Adv. Differ. Equ., 2020 (2020) · Zbl 1485.54041 · doi:10.1186/s13662-020-02819-2
[16] Afshari, H., Solution of fractional differential equations in quasi-b metric and b-metric-like spaces, Adv. Differ. Equ., 2018 (2018) · Zbl 1485.34192 · doi:10.1186/s13662-019-2227-9
[17] Afshari, H.; Kalantari, S.; Karapinar, E., Solution of fractional differential equations via coupled fixed point, Electron. J. Differ. Equ., 2015, 286 (2015) · Zbl 1328.47081
[18] Adiguzel, R. S.; Aksoy, U.; Karapinar, E.; Erhan, I. M., On the solutions of fractional differential equations via Geraghty type hybrid contractions, Appl. Comput. Math., 20, 2, 313-333 (2021) · Zbl 1541.34006
[19] Adiguzel, R. S.; Aksoy, U.; Karapinar, E.; Erhan, I. M., On the solution of a boundary value problem associated with a fractional differential equation, Math. Methods Appl. Sci. (2020) · Zbl 1490.34012 · doi:10.1002/mma.665
[20] Afshari, H.; Karapınar, E., A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces, Adv. Differ. Equ., 2020 (2020) · Zbl 1486.34009 · doi:10.1186/s13662-020-03076-z
[21] Sevinik-Adıgüzel, R.; Aksoy, Ü.; Karapinar, E.; Erhan, I. M., Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions, RACSAM, 115 (2021) · Zbl 1490.34012 · doi:10.1007/s13398-021-01095-3
[22] Karapinar, E.; Binh, H. D.; Luc, N. H.; Can, N. H., On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems, Adv. Differ. Equ., 2021 (2021) · Zbl 1487.35407 · doi:10.1186/s13662-021-03232-z
[23] Afshari, H.; Shojaat, H.; Siahkali Moradi, M., Existence of the positive solutions for a tripled system of fractional differential equations via integral boundary conditions, Res. Nonlinear Anal., 4, 3, 186-199 (2021) · doi:10.53006/rna.938851
[24] Jangid, N.; Joshi, S.; Purohit, S. D.; Suthar, D. L., Fractional derivatives and expansion formulae of incomplete H and H̄-functions, Adv. Theory Nonlinear Anal. Appl., 5, 2, 193-202 (2021) · Zbl 1513.33006 · doi:10.31197/atnaa.755309
[25] Miller, K. S.; Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equation (1993), New York: Wiley, New York · Zbl 0789.26002
[26] Smart, D. R., Fixed Point Theorems (1990), Cambridge: Cambridge University Press, Cambridge · Zbl 0427.47036
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