Research article

Lyapunov-type inequalities for Hadamard fractional differential equation under Sturm-Liouville boundary conditions

  • Received: 02 December 2020 Accepted: 04 January 2021 Published: 08 January 2021
  • MSC : 26A33, 34A08, 34A40, 34B05

  • In this paper, we establish new Lyapunov-type inequalities for a Hadamard fractional differential equation under Sturm-Liouville boundary conditions. Our conclusions cover many results in the literature.

    Citation: Youyu Wang, Lu Zhang, Yang Zhang. Lyapunov-type inequalities for Hadamard fractional differential equation under Sturm-Liouville boundary conditions[J]. AIMS Mathematics, 2021, 6(3): 2981-2995. doi: 10.3934/math.2021181

    Related Papers:

  • In this paper, we establish new Lyapunov-type inequalities for a Hadamard fractional differential equation under Sturm-Liouville boundary conditions. Our conclusions cover many results in the literature.



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    [1] A. M. Lyapunov, Probleme g$\rm\acute{e}$n$\rm\acute{e}$ral de la stabilit$\rm\acute{e}$ du mouvement, Ann. Fac. Sci. Univ., 2 (1907), 27–247.
    [2] R. A. C. Ferreira, A Lyapunov-type inequality for a fractional boundary value problem, Fract. Calc. Appl. Anal., 16, (2013), 978–984.
    [3] R. A. C. Ferreira, On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function, J. Math. Anal. Appl., 412 (2014), 1058–1063.
    [4] R. C. Brown, D. B. Hinton, Lyapunov inequalities and their applications, Dordrecht: Springer, 2000.
    [5] S. K. Ntouyas, B. Ahmad, T. P. Horikis, Recent developments of Lyapunov-type inequalities for fractional differential equations, In: Differential and integral inequalities, Cham: Springer, 2019,619–686.
    [6] S. Dhar, Q. Kong, Lyapunov-type inequalities for third-order half-linear equations and applications to boundary value problems, Nonlinear Anal., 110 (2014), 170–181. doi: 10.1016/j.na.2014.07.020
    [7] S. Dhar, Q. Kong, Lyapunov-type inequalities for higher order half-linear differential equations, Appl. Math. Comput., 273 (2016), 114–124.
    [8] X. Meng, M. Stynes, Green's functions, positive solutions, and a Lyapunov inequality for a Caputo fractional-derivative boundary value problem, Fract. Calc. Appl. Anal., 22 (2019), 750–766. doi: 10.1515/fca-2019-0041
    [9] M. Jleli, B. Samet, Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions, Math. Inequal. Appl., 18 (2015), 443–451.
    [10] M. Jleli, L. Ragoub, B. Samet, Lyapunov-type inequality for a fractional differential equation under a Robin boundary conditions, J. Funct. Space., 2015 (2015), 1–5.
    [11] A. Tiryaki, Recent development of Lyapunov-type inequalities, Adv. Dyn. Syst. Appl., 5 (2010), 231–248.
    [12] Y. Wang, S. Liang, C. Xia, A Lyapunov-type inequality for a fractional differential equation under Sturm-Liouville boundary conditions, Math. Inequal. Appl., 20 (2017), 139–148.
    [13] Y. Wang, Q. Wang, Lyapunov-type inequalities for fractional differential equations under multi-point boundary conditions, J. Math. Inequal., 13 (2019), 611–619.
    [14] Y. Wang, Q. Wang, Lyapunov-type inequalities for nonlinear differential equation with Hilfer fractional derivative operator, J. Math. Inequal., 12 (2018), 709–717.
    [15] Y. Wang, Q. Wang, Lyapunov-type inequalities for nonlinear fractional differential equation with Hilfer fractional derivative under multi-point boundary conditions, Fract. Calc. Appl. Anal., 21 (2018), 833–843. doi: 10.1515/fca-2018-0044
    [16] J. Hadamard, Essai sur l'etude des fonctions donnees par leur developpment de Taylor, J. Math. Pure Appl., 8 (1892), 101–186.
    [17] P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Compositions of Hadamard-type fractional integration operators and the semigroup property, J. Math. Anal. Appl., 269 (2002), 387–400. doi: 10.1016/S0022-247X(02)00049-5
    [18] P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Fractional calculus in the Mellin setting and Hadamard-type fractional integrals, J. Math. Anal. Appl., 269 (2002), 1–27. doi: 10.1016/S0022-247X(02)00001-X
    [19] P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl., 270 (2002), 1–15. doi: 10.1016/S0022-247X(02)00066-5
    [20] F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modification of the Hadamard fractional derivatives, Adv. Differ. Equ., 2012 (2012), 142. doi: 10.1186/1687-1847-2012-142
    [21] A. A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc., 38 (2001), 1191–1204.
    [22] A. A. Kilbas, J. J. Trujillo, Hadamard-type integrals as G-transforms, Integr. Transf. Spec. F., 14 (2003), 413–427. doi: 10.1080/1065246031000074443
    [23] Q. Ma, C. Ma, J. Wang, A Lyapunov-type inequality for a fractional differential equation with Hadamard derivative, J. Math. Inequal., 11 (2017), 135–141.
    [24] S. Dhar, On linear and non-linear fractional Hadamard boundary value problems, Differ. Equ. Appl., 10 (2018), 329–339.
    [25] Z. Laadjal, N. Adjeroud, Q. Ma, Lyapunov-type inequality for the Hadamard fractional boundary value problem on a general interval $[a, b]$, J. Math. Inequal., 13 (2019), 789–799.
    [26] J. Jonnalagadda, B. Debananda, Lyapunov-type inequalities for Hadamard type fractional boundary value problems, AIMS Mathematics, 5 (2020), 1127–1146. doi: 10.3934/math.2020078
    [27] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Amsterdam: Elsevier, 2006.
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