Lyapunov-type inequalities for fractional differential equations

Sha Li; Xu Han; Qiaoluan Li

Sha Li College of Mathematics and Information Science, Hebei Normal University Shijiazhuang, 050024, China
Xu Han College of Mathematics and Information Science, Hebei Normal University Shijiazhuang, 050024, China
Qiaoluan Li College of Mathematics and Information Science, Hebei Normal University Shijiazhuang, 050024, China

Keywords: Lyapunov-type inequalities, Fractional differential equations, Riemann-Liouville derivative, Green's function, Boundary conditions

Abstract

The principal aim of this paper is to discuss Lyapunov-type inequalities for fractional differential equations with fractional boundary conditions. Some new Lyapunov's inequalities are established, which almost generalize and improve some earlier results in the literature.

Downloads

Download data is not yet available.

References

[1] Lyapunov,AM (1907). Probleme general de la stabilitedu mouvement. Ann. Fac. Sci. Univ.,Toulouse 2, 203-407.
[2] Borg, G(1949).On a Liapunoff criterion of stability.Amer. J. Math.,71, 67-70.
[3] Kwong, MK(1981).On Lyapunovs inequality for disfocality. J. Math. Anal. Appl.,83,486-494.
[4] Arifi, NA, Altun, I, Jleli, M, Lashin, A, Samet,B(2016). Lyapunov-type inequalities for a fractional p-Laplacian equation. J. Inequal. Appl.,2016(1),189.
[5] Napoli, PL, Pinasco, JP(2006).Estimates for eigenvalues of quasilinear elliptic systems.J. Differential Equations.,227 ,102-115.
[6] Awarwal, RP, Ozbekler,A(2017). Lyapunov type inequalities for mixed nonlinear Riemann-Liouville fractional differential equations with a forcing term.J. Comput. Appl. Math.,314 ,69-78.
[7] Ferreira, RAC(2013). A Lyapunov-type inequality for a fractional boundary value problem.Fract. Calc. Appl. Anal.,16 (4),978-984.
[8] Reid, TW(1965). A matrix equation related to an non-oscillation criterion and Lyapunov stability.Quart. Appl. Math. Soc.,23 ,83-87.
[9] Reid,TW(1970). A matrix Lyapunov inequality.J. Math. Anal. Appl.,32 ,424-434.
[10] Nehari,Z(1959).Some eigenvalue estimates. J. Anal. Math.,7 ,79-88.