Further results on Sturm-Picone theorems for nonlinear fractional differential equations

Authors

  • John R. Graef University of Tennessee at Chattanooga

DOI:

https://doi.org/10.31349/RevMexFis.72.030201

Abstract

The author obtains Sturm-Picone comparison results for fractional differential equations involving conformable and nonconformable fractional derivatives. Examples illustrate the conclusions.

Downloads

Download data is not yet available.

References

T. Abdeljawad, On conformable fractional calculus, J. Comp. Appl. Math. 279 (2015) 57-66 DOI: https://doi.org/10.1016/j.cam.2014.10.016

R. P. Agarwal, S. R. Grace, and D. O’Regan, Oscillation Theory for Second Order, Linear, Half-Linear, Superlinear, and Sublinear Dynamic Equations, (Kluwer, Dordrecht, 2002) DOI: https://doi.org/10.1007/978-94-017-2515-6

N. Aguila-Camacho, M. A. Duarte-Mermoud, J. A. Gallegos, Lyapunov functions for fractional order systems, Commun. Nonlinear Sci. Numer. Simulat. 19 (2014) 2951-2957 DOI: https://doi.org/10.1016/j.cnsns.2014.01.022

A. Fleitas, J. E. Napoles Vald ´ es, J. M. Rodríguez, and J. M. Sigarreta-Almira, Note on the generalized conformable derivative, Rev. Un. Mat. Argentina 62 (2021) 443-457 DOI: https://doi.org/10.33044/revuma.1930

A. Fleitas, J. A. Méndez-Bermuez, J. E. Nápoles Valdés, J. M. Sigarreta-Almira, On fractional Lienard type systems, Rev. Mex. Fís. 65 (2019) 618-625 DOI: https://doi.org/10.31349/RevMexFis.65.618

J. R. Graef, The limit-point/limit-circle problem for fractional differential equations, Nonlinear. Dyn. Syst. Theory, to appear

J. R. Graef, A nonlinear Sturm-Picone theorem for fractional differential equations, to appear

J. R. Graef and P. W. Spikes, Continuability, boundedness, and asymptotic behavior of solutions of x 00+q(t)f(x) = r(t), Ann. Mat. Pura Appl. 101 (1974) 307-320 DOI: https://doi.org/10.1007/BF02417110

J. R. Graef and P. W. Spikes, Boundedness and convergence to zero of solutions of a forced second order nonlinear differential equation, J. Math. Anal. Appl. 62 (1978) 295-309 DOI: https://doi.org/10.1016/0022-247X(78)90127-0

P. M. Guzmán, L. M. L. M. Bittencurt, and J. E. Nápoles Valdés, A note on stability of certain Lienard fractional equation, Int. J. Math. Comput. Sci. 14 (2019) 301-315

P. M. Guzmán, L. M. L. M. Bittencurt, and J. E. Nápoles Valdés, On the stability of solutions of fractional non conformable differential equations, preprint

P. M. Guzmán, G. Langton, L. M. L. M. Bittencurt, J. Medina, and J. E. Nápoles Valdés, A new definition of a fractional derivative of local type, J. Math. Anal. 9 (2018) 88-98

P. M. Guzmán and J. E. Nápoles Valdés, A note on the oscillatory character of some non conformable generalized Lienard system, Adv. Math. Models Appl. 4 (2019) 127-133

R. Khalil, M. A. Horani, A. Yousef, and M Sababheh, A new definition of fractional derivative, J. Comp. Appl. Math. 264 (2014) 65-70 DOI: https://doi.org/10.1016/j.cam.2014.01.002

Y. Khurshid, M. A. Khan, and Y. M. Chu, Conformable fractional integral inequalities for GG- and GA-convex functions, AIMS Mathematics 5 (2020) 5012-5030 DOI: https://doi.org/10.3934/math.2020322

F. Martínez, I. Martínez, M. K. A. Kaabar, and S Paredes, Note on the conformable boundary value problems: Sturm’s theorem and Green’s function, Rev. Mex. Fis. 67 (2021) 471-481 DOI: https://doi.org/10.31349/RevMexFis.67.471

F. Martínez and J. E. Nápoles Valdés, Towards a non-conformable fractional calculus of n-variables. J. Math. 43 (2020) 87-98 DOI: https://doi.org/10.7862/rf.2020.6

J. E. Nápoles Valdés, Boundedness and global asymptotic stability of the forced Lienard equation Rev. Un. Mat. Argentina 41 (2000) 47-59

J. E. Nápoles Valdés and M. N. Q. Cubillos, On the oscillatory nature of some generalized Emden-Fowler equation, Punjab Univ. J. Math. (Lahore) 52 (2020) 97-106

J. E. Nápoles Valdés, P. M. Guzmán, and L. M. Lugo, Some new results on nonconformable fractional calculus, Adv. Dyn. Syst. Appl. 13 (2018) 167-175

J. E. Nápoles Valdés, P. M. Guzmán, and L. M. Lugo, On the stability of solutions of nonconformable differential equations, Stud. Univ. Babeş-Bolyai Math. 65 (2020) 495-502 DOI: https://doi.org/10.24193/subbmath.2020.4.02

J. E. Nápoles Valdés and C. Tunç, On the boundedness and oscillation of non-conformable Lienard equation, J. Fract. Calc. Appl. 11 (2020) 92-101 DOI: https://doi.org/10.3390/sym11091108

M. Picone, Sui valori eccezionali di un parametro da cui dipend un‘equazione differenziale linear ordinaria del second ordine, Ann. Scuola Norm. Sup. Pisa 11 (1910) 1-144

C. Sturm, Sur les equations differentielles lineaires du second ordre, Math. Pures Appl. 1 (1836) 106-186. 25. C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, (Academic Press, New York, 1968).

Downloads

Published

2026-05-01

How to Cite

[1]
J. Graef, “Further results on Sturm-Picone theorems for nonlinear fractional differential equations”, Rev. Mex. Fís., vol. 72, no. 3, pp. 030201–030204, May 2026.