Research Article

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

Volume: 47 Number: 6 December 12, 2018
  • Maysaa Al-qurashi
  • Lakhdar Ragoub *
EN

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

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

References

  1. El-Shahed, M., Positive solutions for boundary value problem of nonlinear fractional differential equation, Abstr. Appl. Anal., Article ID 10368, 8 pp., 2007.
  2. Ferreira, R. A. C., A Lyapunov-type inequality for a fractional boundary value problem, Fract. Calc. Appl. Anal. 16 (4), 978-984, 2013.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Lyapunov, A. M., Probleme general de la stabilite du mouvement, Ann. Fac. Sci. Univ. Toulouse. 2, 203-407, 1907.
  8. Pachpatte, B. G., Mathematical Inequalities, North Holland Mathematical Library 67, Elsevier, xii+591 pp, 2005.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Maysaa Al-qurashi This is me

Lakhdar Ragoub * This is me

Publication Date

December 12, 2018

Submission Date

May 18, 2015

Acceptance Date

April 1, 2016

Published in Issue

Year 2018 Volume: 47 Number: 6

APA
Al-qurashi, M., & Ragoub, L. (2018). Lyapunov-type inequality for a Riemann-Liouville fractional differential boundary value problem. Hacettepe Journal of Mathematics and Statistics, 47(6), 1447-1452. https://izlik.org/JA33JB93XG
AMA
1.Al-qurashi M, Ragoub L. Lyapunov-type inequality for a Riemann-Liouville fractional differential boundary value problem. Hacettepe Journal of Mathematics and Statistics. 2018;47(6):1447-1452. https://izlik.org/JA33JB93XG
Chicago
Al-qurashi, Maysaa, and Lakhdar Ragoub. 2018. “Lyapunov-Type Inequality for a Riemann-Liouville Fractional Differential Boundary Value Problem”. Hacettepe Journal of Mathematics and Statistics 47 (6): 1447-52. https://izlik.org/JA33JB93XG.
EndNote
Al-qurashi M, Ragoub L (December 1, 2018) Lyapunov-type inequality for a Riemann-Liouville fractional differential boundary value problem. Hacettepe Journal of Mathematics and Statistics 47 6 1447–1452.
IEEE
[1]M. Al-qurashi and L. Ragoub, “Lyapunov-type inequality for a Riemann-Liouville fractional differential boundary value problem”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1447–1452, Dec. 2018, [Online]. Available: https://izlik.org/JA33JB93XG
ISNAD
Al-qurashi, Maysaa - Ragoub, Lakhdar. “Lyapunov-Type Inequality for a Riemann-Liouville Fractional Differential Boundary Value Problem”. Hacettepe Journal of Mathematics and Statistics 47/6 (December 1, 2018): 1447-1452. https://izlik.org/JA33JB93XG.
JAMA
1.Al-qurashi M, Ragoub L. Lyapunov-type inequality for a Riemann-Liouville fractional differential boundary value problem. Hacettepe Journal of Mathematics and Statistics. 2018;47:1447–1452.
MLA
Al-qurashi, Maysaa, and Lakhdar Ragoub. “Lyapunov-Type Inequality for a Riemann-Liouville Fractional Differential Boundary Value Problem”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, Dec. 2018, pp. 1447-52, https://izlik.org/JA33JB93XG.
Vancouver
1.Maysaa Al-qurashi, Lakhdar Ragoub. Lyapunov-type inequality for a Riemann-Liouville fractional differential boundary value problem. Hacettepe Journal of Mathematics and Statistics [Internet]. 2018 Dec. 1;47(6):1447-52. Available from: https://izlik.org/JA33JB93XG