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Lyapunov-type inequalities for higher-order Caputo fractional differential equations with general two-point boundary conditions.(English)Zbl 07910619

Summary: In this paper the authors present three different Lyapunov-type inequalities for a higher-order Caputo fractional differential equation with identical boundary conditions marking the inaugural instance of such an approach in the existing literature. Their findings extend and complement certain prior ress in the literature.

MSC:

34A08 Fractional ordinary differential equations
26D10 Inequalities involving derivatives and differential and integral operators
34B15 Nonlinear boundary value problems for ordinary differential equations

Cite

References:

[1]R. P. Agarwal, Y. Liu, D. O’Regan, and C. Tian, “Positive solutions of two-point boundary value problems for fractional singular differential equations,” Differ. Equ., vol. 48, no. 5, pp. 619-629, 2012, translation of Differ. Uravn. 48 (2012), no. 5, 611-621. ·Zbl 1263.34009
[2]R. P. Agarwal, M. Bohner, and A. Özbekler, Lyapunov inequalities and applications. Springer, Cham, 2021, doi: 10.1007/978-3-030-69029-8. ·Zbl 1470.35001 ·doi:10.1007/978-3-030-69029-8
[3]M. F. Aktaş and D. Çakmak, “Lyapunov-type inequalities for third-order linear differential equations,” Electron. J. Differential Equations, 2017, Art. ID 139. ·Zbl 1370.34056
[4]M. F. Aktaş and D. Çakmak, “Lyapunov-type inequalities for third-order linear differential equations under the non-conjugate boundary conditions,” Differ. Equ. Appl., vol. 10, no. 2, pp. 219-226, 2018, doi: 10.7153/dea-2018-10-14. ·Zbl 1400.34029 ·doi:10.7153/dea-2018-10-14
[5]M. F. Aktaş and D. Çakmak, “Lyapunov-type inequalities for third order linear differential equations with two points boundary conditions,” Hacet. J. Math. Stat., vol. 48, no. 1, pp. 59-66, 2019, doi: 10.15672/hjms.2017.514. ·Zbl 1471.34063 ·doi:10.15672/hjms.2017.514
[6]M. Bohner, A. Domoshnitsky, S. Padhi, and S. N. Srivastava, “Vallée-Poussin theorem for equations with Caputo fractional derivative,” Math. Slovaca, vol. 73, no. 3, pp. 713-728, 2023, doi: 10.1515/ms-2023-0052. ·Zbl 1516.34098 ·doi:10.1515/ms-2023-0052
[7]I. Cabrera, B. Lopez, and K. Sadarangani, “Lyapunov type inequalities for a fractional two-point boundary value problem,” Math. Methods Appl. Sci., vol. 40, no. 10, pp. 3409-3414, 2017, doi: 10.1002/mma.4232. ·Zbl 1375.34004 ·doi:10.1002/mma.4232
[8]S. Dhar and Q. Kong, “Lyapunov-type inequalities for third-order linear differential equations,” Math. Inequal. Appl., vol. 19, no. 1, pp. 297-312, 2016, doi: 10.7153/mia-19-22. ·Zbl 1345.34029 ·doi:10.7153/mia-19-22
[9]S. Dhar and Q. Kong, “Fractional Lyapunov-type inequalities with mixed boundary conditions on univariate and multivariate domains,” J. Fract. Calc. Appl., vol. 11, no. 2, pp. 148-159, 2020. ·Zbl 1499.34042
[10]A. Domoshnitsky, S. Padhi, and S. N. Srivastava, “Vallée-Poussin theorem for fractional func-tional differential equations,” Fract. Calc. Appl. Anal., vol. 25, no. 4, pp. 1630-1650, 2022, doi: 10.1007/s13540-022-00061-z. ·Zbl 1503.34143 ·doi:10.1007/s13540-022-00061-z
[11]J. R. Graef, K. Maazouz, and M. D. A. Zaak, “A generalized Lyapunov inequality for a pan-tograph boundary value problem involving a variable order Hadamard fractional derivative,” Mathematics, vol. 11, no. 13, 2023, Art. ID 2984, doi: 10.3390/math11132984. CUBO 26, 2 (2024) ·doi:10.3390/math11132984
[12]J. R. Graef, R. Mahmoud, S. H. Saker, and E. Tunç, “Some new Lyapunov-type inequalities for third order differential equations,” Comm. Appl. Nonlinear Anal., vol. 22, no. 2, pp. 1-16, 2015. ·Zbl 1326.34042
[13]A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differ-ential equations, ser. North-Holland Mathematics Studies. Elsevier Science B.V., Amsterdam, 2006, vol. 204. ·Zbl 1092.45003
[14]A. M. Lyapunov, “Probléme général de la stabilité du mouvement,” Ann. Fac. Sci. Toulouse Math., vol. 9, pp. 203-474, 1907. ·JFM 38.0738.07
[15]Q. Ma, C. Ma, and J. Wang, “A Lyapunov-type inequality for a fractional differential equa-tion with Hadamard derivative,” J. Math. Inequal., vol. 11, no. 1, pp. 135-141, 2017, doi: 10.7153/jmi-11-13. ·Zbl 1361.34009 ·doi:10.7153/jmi-11-13
[16]A. D. Oğuz, J. Alzabut, A. Özbekler, and J. M. Jonnalagadda, “Lyapunov and Hartman-type inequalities for higher-order discrete fractional boundary value problems,” Miskolc Math. Notes, vol. 24, no. 2, pp. 953-963, 2023, doi: 10.18514/mmn.2023.3931. ·Zbl 1549.39012 ·doi:10.18514/mmn.2023.3931
[17]N. Parhi and S. Panigrahi, “On Liapunov-type inequality for third-order differential equations,” J. Math. Anal. Appl., vol. 233, no. 2, pp. 445-460, 1999, doi: 10.1006/jmaa.1999.6265. ·Zbl 0932.34030 ·doi:10.1006/jmaa.1999.6265
[18]I. Podlubny, Fractional differential equations, ser. Mathematics in Science and Engineering. Academic Press, Inc., San Diego, CA, 1999, vol. 198. ·Zbl 0924.34008
[19]T. Qiu and Z. Bai, “Existence of positive solutions for singular fractional differential equations,” Electron. J. Differential Equations, 2008, Art. ID 146. ·Zbl 1172.34313
[20]T. Qiu and Z. Bai, “Positive solutions for boundary value problem of nonlinear frac-tional differential equation,” J. Nonlinear Sci. Appl., vol. 1, no. 3, pp. 123-131, 2008, doi: 10.22436/jnsa.001.03.01. ·Zbl 1173.34314 ·doi:10.22436/jnsa.001.03.01
[21]J. Rong and C. Bai, “Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions,” Adv. Difference Equ., 2015, Art. ID 82, doi: 10.1186/s13662-015-0430-x. ·Zbl 1343.34021 ·doi:10.1186/s13662-015-0430-x
[22]S. N. Srivastava, S. Pati, S. Padhi, and A. Domoshnitsky, “Lyapunov inequality for a Caputo fractional differential equation with Riemann-Stieltjes integral boundary conditions,” Math. Methods Appl. Sci., vol. 46, no. 12, pp. 13 110-13 123, 2023, doi: 10.1002/mma.9238. ·Zbl 1528.34010 ·doi:10.1002/mma.9238
[23]Y. Sun and X. Zhang, “Existence and nonexistence of positive solutions for fractional-order two-point boundary value problems,” Adv. Difference Equ., 2014, Art. ID 53, doi: 10.1186/1687-1847-2014-53. ·Zbl 1343.34022 ·doi:10.1186/1687-1847-2014-53
[24]C. Tian and Y. Liu, “Multiple positive solutions for a class of fractional singular boundary value problems,” Mem. Differ. Equ. Math. Phys., vol. 56, pp. 115-131, 2012. ·Zbl 1298.34019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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