×

Variational approach to \(p\)-Laplacian fractional differential equations with instantaneous and non-instantaneous impulses. (English) Zbl 1441.34021

Summary: In this paper, we study the existence of solutions for fractional differential equations of \(p\)-Laplacian with instantaneous and non-instantaneous impulses. The existence of solutions for a class of fractional differential equations with instantaneous and non-instantaneous impulses is obtained by using the critical point theory. Finally, an example is given to illustrate the feasibility of the main results.

MSC:

34A08 Fractional ordinary differential equations
34A37 Ordinary differential equations with impulses
34B37 Boundary value problems with impulses for ordinary differential equations
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Agarwal, R.; Hristova, S.; O’Regan, D., Non-Instantaneous Impulses in Differential Equations (2017), Springer: Springer Cham · Zbl 1411.34031
[2] Yan, Q. S., Periodic optimal control problems governed by semilinear parabolic equations with impulse control, Acta Math., 15, 847-862 (2016) · Zbl 1363.49031
[3] Nieto, J. J.; Liang, B., Variational approach to differential equations with not instantaneous impulses, Appl. Math. Lett., 73, 44-48 (2017) · Zbl 1382.34028
[4] Khaliq, A.; Rehman, MU., On variational methods to non-instantaneous impulsive fractional differential equation, Appl. Math. Lett., 83, 95-102 (2018) · Zbl 1489.34017
[5] Pei, Y.; Martin, B.; Dechang, P., Impulsive synchronization of time-scales complex networks with time-varying topology, Nonlinear Anal., 35, 3-22 (2019)
[6] Huang, X.; Cao, J., Quasi-synchronization of neural networks with parameter mismatches and delayed impulsive controller on time scales, Nonlinear Anal. RWA, 33, 104-115 (2019) · Zbl 1429.93160
[7] Xiao, J.; Nieto, J. J.; Luo, Z. G., Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods, Commun. Nonlinear Sci. Numer. Numer. Simul., 17, 426-432 (2012) · Zbl 1251.34046
[8] Tang, Q.; Nieto, J. J., Variational approach to impulsive evolution equations, Appl. Math. Lett., 36, 31-55 (2014) · Zbl 1321.34079
[9] Yang, P.; Wang, J. R.; ORegan, D.; Feckan, M., Inertial manifold for semi-linear non-instantaneous impulsive parabolic equations in an admissible space, Commun. Nonlinear Sci. Numer. Simul., 75, 174-191 (2019) · Zbl 1509.35067
[10] Tian, Y.; Zhang, M., Variational method to differential equations with instantaneous and non-instantaneous impulses, Appl. Math. Lett., 94, 160-165 (2019) · Zbl 1418.34036
[11] Zhang, W.; Liu, W., Variational approach to fractional Dirichlet problem with instantaneous and non-instantaneous impulses, Appl. Math. Lett., 99, 105-111 (2019)
[12] Zhou, Y.; Wang, J. R.; Zhang, L., Basic Theory of Fractional Differential Equations (2017), World Scientific Publishing Co. Pte. Ltd.: World Scientific Publishing Co. Pte. Ltd. Hackensack, NJ · Zbl 1360.34003
[13] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., (Theory Andapplications of Fractional Differential Equations. Theory Andapplications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204 (2006), Elsevier Science B.V.: Elsevier Science B.V. Amsterdam) · Zbl 1092.45003
[14] Jiao, F.; Zhou, Y., Existence results for fractional boundary value problem via critical point theory, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 22, 17 (2012) · Zbl 1258.34015
[15] Zhou, Y., Basic Theory of Fractional Differential Equations (2016), Springer: Springer Cham
[16] Mawhin, J.; Willem, M., Critical Point Theorey and Hamiltonian Systems (1989), Springer: Springer New York · Zbl 0676.58017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.