Research Article

Novel Lyapunov-type inequality for fractional boundary value problem

Volume: 2 Number: 2 February 24, 2020
EN

Novel Lyapunov-type inequality for fractional boundary value problem

Abstract

In this paper, we establish a new Lyapunov-type inequality for a differential equation involving Caputo fractional derivatives subject to non-local boundary conditions. As an application to the corresponding eigenvalue problem is also discussed.

Keywords

References

  1. Abdeljawad, T., Alzabut, J. & Jarad, F. A generalized Lyapunov-type inequality in the frame of conformable derivatives. Adv Differ Equ 2017, 321 (2017)
  2. R. A. C. Ferreira, Novel Lyapunov-type inequalities for sequential fractional boundary value problems, RACSAM Rev. R. Acad. A, 113 (2019), 171--179.
  3. A. Guezane-Lakoud, R. Khaldi and D. F.M. Torres, Lyapunov-type inequality for a fractional boundary value problem with natural conditions, SeMA (2018) 75:157--162
  4. R. Khaldi and A Guezane-Lakoud, On a generalized Lyapunov inequality for a mixed fractional boundary value problem, AIMS Mathematics, 4(3): 506--515.
  5. R. Khaldi and A Guezane-Lakoud, Lyapunov inequality for a boundary value problem involving conformable derivative, Prog. Frac. Diff. Appl. 3 (2017), No. 4, 323-329.
  6. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
  7. A. M. Lyapunov, Problème général de la stabilité du mouvement, (French Translation of a Russian paper dated 1893), Ann. Fac. Sci. Univ. Toulouse 2 (1907), 27--247, Reprinted as Ann. Math. Studies, No, 17, Princeton, 1947.
  8. Ntouyas S.K., Ahmad B., Horikis T.P. (2019) Recent Developments of Lyapunov--Type Inequalities for Fractional Differential Equations. In: Andrica D., Rassias T. (eds) Differential and Integral Inequalities. Springer Optimization and Its Applications, vol 151. Springer, Cham

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

February 24, 2020

Submission Date

December 16, 2019

Acceptance Date

February 20, 2020

Published in Issue

Year 2019 Volume: 2 Number: 2

APA
Khaldi, R. (2020). Novel Lyapunov-type inequality for fractional boundary value problem. Journal of Multidisciplinary Modeling and Optimization, 2(2), 65-70. https://izlik.org/JA92EH29AS
AMA
1.Khaldi R. Novel Lyapunov-type inequality for fractional boundary value problem. jmmo. 2020;2(2):65-70. https://izlik.org/JA92EH29AS
Chicago
Khaldi, Rabah. 2020. “Novel Lyapunov-Type Inequality for Fractional Boundary Value Problem”. Journal of Multidisciplinary Modeling and Optimization 2 (2): 65-70. https://izlik.org/JA92EH29AS.
EndNote
Khaldi R (February 1, 2020) Novel Lyapunov-type inequality for fractional boundary value problem. Journal of Multidisciplinary Modeling and Optimization 2 2 65–70.
IEEE
[1]R. Khaldi, “Novel Lyapunov-type inequality for fractional boundary value problem”, jmmo, vol. 2, no. 2, pp. 65–70, Feb. 2020, [Online]. Available: https://izlik.org/JA92EH29AS
ISNAD
Khaldi, Rabah. “Novel Lyapunov-Type Inequality for Fractional Boundary Value Problem”. Journal of Multidisciplinary Modeling and Optimization 2/2 (February 1, 2020): 65-70. https://izlik.org/JA92EH29AS.
JAMA
1.Khaldi R. Novel Lyapunov-type inequality for fractional boundary value problem. jmmo. 2020;2:65–70.
MLA
Khaldi, Rabah. “Novel Lyapunov-Type Inequality for Fractional Boundary Value Problem”. Journal of Multidisciplinary Modeling and Optimization, vol. 2, no. 2, Feb. 2020, pp. 65-70, https://izlik.org/JA92EH29AS.
Vancouver
1.Rabah Khaldi. Novel Lyapunov-type inequality for fractional boundary value problem. jmmo [Internet]. 2020 Feb. 1;2(2):65-70. Available from: https://izlik.org/JA92EH29AS