Abstract
In this work, we derive a Lyapunov-type inequality for a fractional problem depending on an integral boundary condition. We believe our results to be new even for the classical integer-order derivative case.
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References
I. Cabrera, K. Sadarangani, B. Samet, Hartman-Wintner-type inequalities for a class of nonlocal fractional boundary value problems. Math. Methods Appl. Sci. 40(1), 129–136 (2017)
S. Dhar, Q. Kong, M. McCabe, Fractional boundary value problems and Lyapunov-type inequalities with fractional integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. 2016, no. 43, 16 p
R.A.C. Ferreira, A Lyapunov-type inequality for a fractional boundary value problem. Fract. Calc. Appl. Anal. 16(4), 978–984 (2013)
R.A.C. Ferreira, On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function. J. Math. Anal. Appl. 412(2), 1058–1063 (2014)
R.A.C. Ferreira, Lyapunov-type inequalities for some sequential fractional boundary value problems. Adv. Dyn. Syst. Appl. 11(1), 33–43 (2016)
R.A.C. Ferreira, Existence and uniqueness of solutions for two-point fractional boundary value problems. Electron. J. Differ. Equ. 2016, Paper No. 202, 5 p
R.A.C. Ferreira, Lyapunov-type inequality for an anti-periodic fractional boundary value problem. Fract. Calc. Appl. Anal. 20(1), 284–291 (2017)
R.A.C. Ferreira, RACSAM (2018). https://doi.org/10.1007/s13398-017-0462-z
M. Jleli, B. Samet, Lyapunov-type inequalities for fractional boundary-value problems. Electron. J. Differ. Equ. 2015, no. 88, 11 p
M. Jleli, B. Samet, Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions. Math. Inequal. Appl. 18(2), 443–451 (2015)
M. Jleli, M. Kirane, B. Samet, Lyapunov-type inequalities for fractional partial differential equations. Appl. Math. Lett. 66, 30–39 (2017)
M. Jleli, J.J. Nieto, B. Samet, Lyapunov-type inequalities for a higher order fractional differential equation with fractional integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. 2017, Paper No. 16, 17 p
N. Pathak, Lyapunov-type inequality for fractional boundary value problems with Hilfer derivative. Math. Inequal. Appl. 21(1), 179–200 (2018)
J. Rong, C. Bai, Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions. Adv. Differ. Equ. 2015, 2015:82, 10 p
Acknowledgements
Rui Ferreira was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Investigador FCT” with reference IF/01345/2014.
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Ferreira, R.A.C. (2018). Lyapunov Inequalities for Some Differential Equations with Integral-Type Boundary Conditions. In: Agarwal, P., Dragomir, S., Jleli, M., Samet, B. (eds) Advances in Mathematical Inequalities and Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-3013-1_3
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DOI: https://doi.org/10.1007/978-981-13-3013-1_3
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