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

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

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.

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

Abstract

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.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Maysaa Al-qurashi This is me

Lakhdar Ragoub This is me

Publication Date December 12, 2018
Published in Issue Year 2018 Volume: 47 Issue: 6

Cite

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.
AMA Al-qurashi M, Ragoub L. Lyapunov-type inequality for a Riemann-Liouville fractional differential boundary value problem. Hacettepe Journal of Mathematics and Statistics. December 2018;47(6):1447-1452.
Chicago Al-qurashi, Maysaa, and Lakhdar Ragoub. “Lyapunov-Type Inequality for a Riemann-Liouville Fractional Differential Boundary Value Problem”. Hacettepe Journal of Mathematics and Statistics 47, no. 6 (December 2018): 1447-52.
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 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, 2018.
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 2018), 1447-1452.
JAMA 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, 2018, pp. 1447-52.
Vancouver 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):1447-52.