Lyapunov-type inequality for a Riemann-Liouville fractional differential boundary value problem

Year 2018, Volume: 47 Issue: 6, 1447 - 1452, 12.12.2018

Maysaa Al-qurashi Lakhdar Ragoub

https://izlik.org/JA33JB93XG

Abstract

The aim of this paper is to present a Lyapunov-type inequality for a Riemann-Liouville fractional differential equation of order $2<\alpha\leq3$ subject to mixed boundary conditions.

Keywords

Lyapunov's inequality , Riemann-Liouville derivative , Caputo fractional derivative , mixed boundary conditions

References

• El-Shahed, M., Positive solutions for boundary value problem of nonlinear fractional differential equation, Abstr. Appl. Anal., Article ID 10368, 8 pp., 2007.
• Ferreira, R. A. C., A Lyapunov-type inequality for a fractional boundary value problem, Fract. Calc. Appl. Anal. 16 (4), 978-984, 2013.
• Ferreira, R. A. C., On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function, J. Math. Anal. Appl. 412, no. 2, 1058–1063, 2014.
• Jleli, M., Ragoub, L., Samet, B., A Lyapunov-type inequality for a fractional differential equation under a Robin boundary condition, J. Funct. Spaces, Volume 2015, Article ID 468536, 5 pp., 2015.
• Jleli, M., Samet, B., Lyapunov-type inequality for a fractional differential equation with a mixed boundary condition, Math. Ineq. Appl., vol. 18, no. 2, pp. 443–451, 2015.
• Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and applications of fractional differential equations, vol. 204 of North-Holland Mathematics Studies, Elsevier, Amsterdam, xvi+523 pp., 2006.
• Lyapunov, A. M., Probleme general de la stabilite du mouvement, Ann. Fac. Sci. Univ. Toulouse. 2, 203-407, 1907.
• Pachpatte, B. G., Mathematical Inequalities, North Holland Mathematical Library 67, Elsevier, xii+591 pp, 2005.