Geodesic
Oscillation criteria for fractional impulsive hybrid partial differential equations
Problemy analiza, Tome 8 (2019) no. 2, pp. 73-91.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study the oscillatory behavior of the solutions of fractional-order nonlinear impulsive hybrid partial differential equations with the mixed boundary condition. By using the integral averaging method and the Riccati technique, we have obtained the oscillation criteria of all the solutions of the given system. An example is given to illustrate our main results.
Keywords: Fractional partial differential equation, Hybrid differential equation, impulse.
Mots-clés : Oscillation 
@article{PA_2019_8_2_a5,
     author = {V. Sadhasivam and M. Deepa},
     title = {Oscillation criteria for fractional impulsive hybrid partial differential equations},
     journal = {Problemy analiza},
     pages = {73--91},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_2_a5/}
}
TY  - JOUR
AU  - V. Sadhasivam
AU  - M. Deepa
TI  - Oscillation criteria for fractional impulsive hybrid partial differential equations
JO  - Problemy analiza
PY  - 2019
SP  - 73
EP  - 91
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2019_8_2_a5/
LA  - en
ID  - PA_2019_8_2_a5
ER  - 
%0 Journal Article
%A V. Sadhasivam
%A M. Deepa
%T Oscillation criteria for fractional impulsive hybrid partial differential equations
%J Problemy analiza
%D 2019
%P 73-91
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2019_8_2_a5/
%G en
%F PA_2019_8_2_a5
V. Sadhasivam; M. Deepa. Oscillation criteria for fractional impulsive hybrid partial differential equations. Problemy analiza, Tome 8 (2019) no. 2, pp. 73-91. http://geodesic.mathdoc.fr/item/PA_2019_8_2_a5/

[1] Abbas S., Benchora M., N'Guerekata G. M., Topics in fractional differential equations, Springer, New York, 2012 | MR | Zbl

[2] Bainov D. D., Mishev D. P., “Estimates of solutions of impulsive parabolic equations and applications to the population dynamics”, Publ. Math., 40 (1996), 85–94 | DOI | MR | Zbl

[3] Chatzarakis G. E., Sadhasivam V., Raja T., Kalaimani T., “Oscillation of certain nonlinear impulsive neutral partial differential equations with continuous distributed deviating arguments and a damping term”, Dyn. Contin. Discrete Impulsive Syst. Ser. A Math. Anal., 25 (2018), 329–345 | MR | Zbl

[4] Daftardar-Gejji V., Fractional calculus theory and applications, Narosa publishing house Pvt. Ltd, 2014

[5] Dhage B. C., Lakshmikantham V., “Basic results on hybrid differential equations”, Nonlinear Anal. Hybrid syst., 4 (2010), 414–424 | DOI | MR | Zbl

[6] Erbe L., Freedman H., Liu X. Z., Wu J. H., “Comparison principles for impulsive parabolic equations with application to models of single species growth”, J. Aust. Math. Soc., 32 (1991), 382–400 | DOI | MR | Zbl

[7] Feng Q., Meng F., “Oscillation of solutions to nonlinear forced fractional differential equations”, Electron. J. Differential Equations, 169 (2013), 1–10 | MR

[8] Ge H., Xin J., “On the existence of a mild solution for impulsive hybrid fractional differential equations”, Adv. Difference Equ., 211 (2013) | MR

[9] Gopalsamy K., Zhang B. G., “On delay differential equations with impulses”, J. Math. Anal. Appl., 139 (1989), 110–122 | DOI | MR | Zbl

[10] Herzallah M. A. E., Baleanu D., “On fractional order hybrid differential equations”, Abstr. Appl. Anal., Hindawi, 2014, 389386, 7 pp. | MR | Zbl

[11] Heydari M., Loghmani G. B., Hosseini S. M., Karbassi S. M., “Application of hybrid functions for solving diffing-harmonic oscillator”, J. Difference Equ., Hindawi, 2014, 210754, 9 pp.

[12] Jiang G., Lu Q., “Impulsive state feedback control of a predator-prey model”, J. Comput. Appl. Math., 200:1 (2007), 193–207 | DOI | MR | Zbl

[13] Kalaimani T., Raja T., Sadhasivam V., Saker S. H., “Oscillation of impulsive neutral partial differential equations with distributed deviating arguments”, Bull. Math. Soc. Sci. Math. Roumanie, 61:1 (2018), 51–68 | MR | Zbl

[14] Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and applications of fractional differential equations, Elsevier science, B.V., Amsterdam, 2006 | MR | Zbl

[15] Lakshmikantham V., Bainov D. D., Simenov P. S., Theory of impulsive differential equations, World scientific publishers, Singapore, 1989 | MR | Zbl

[16] Li W. N., Sheng W., “Oscillation properties for solutions of a kind of partial fractional differential equations with damping term”, J. Nonlinear Sci Appl., 2016, 1600–1608 | MR | Zbl

[17] Liu W., Ngo Q. A., Huy V. N., “Several interesting integral inequalities”, J. Math. Inequal., 3:2 (2009), 201–212 | DOI | MR

[18] Mainardi F., Fractional calculus and waves in linear viscoelasticity, Imberical college press, London, 2010 | MR

[19] Maleknejad K., Torkzadeh L., “Application of hybrid functions for solving oscillator equations”, Rom. Journ. Phys., 60:1–2 (2015), 87–98

[20] Prakash P., Harikrishnan S., “Oscillation of solutions of impulsive vector hyperbolic differential equations with delays”, Appl. Anal., 91:3 (2012), 459–473 | DOI | MR | Zbl

[21] Prakash P., Harikrishnan S., Nieto J. J., Kim J. H., “Oscillation of a time fractional partial differential equations”, Electron. J. Qual. Theory Differ. Equ., 15 (2014), 1–10 | DOI | MR

[22] Sadhasivam V., Kavitha J., “Forced oscillation of fractional order partial differential equations with damping and functional arguments”, IJPAM, 106:7 (2016), 89–107

[23] Sadhasivam V., Kavitha J., Raja T., “Forced oscillation of impulsive neutral hyperbolic differential equations”, International journal of applied engineering research, 11:1 (2016), 58–63

[24] Sadhasivam V., Kavitha J., Deepa M., “On the oscillation of nonlinear fractional partial differential equations”, Global JPAM, 13:5 (2017), 223–231

[25] Sadhasivam V., Raja T., Kalaimani T., “Oscillation of system of impulsive neutral partial differential equations with damping term”, IJPAM, 115:9 (2017), 65–81

[26] Samko S. G., Kilbas A. A., Marichev O. I., Fractional integrals and derivatives, Gordon and breach science publishers, Yverdon, 1993 | MR | Zbl

[27] Sitho S., Ntouyas S. K., Tariboon J., “Existence results for hybrid fractional integro-differential equations”, Bound. Value Probl., 113 (2015), 1–13 | MR

[28] Vasundara Devi J., Giribabu N., “On hybrid Caputo fractional differential equations with variable moments of impulse”, Eur. J. Pure Appl. Math., 7:2 (2014), 115–128 | MR

[29] Wu J., Theory and applications of partial functional differential equations, Springer, New York, 1996 | MR | Zbl

[30] Yang J., Liu A., Liu G., “Oscillation of solutions to neutral nonlinear impulsive hyperbolic equations with several delays”, Electron. J. Differ. Eq., 27 (2013), 1–10 | MR

[31] Yoshida N., Oscillation theory of partial differential equations, World Scientific, Singapore, 2008 | MR | Zbl

[32] Zhao Y., Sun S., Han Z., Li Q., “Theory of fractional hybrid differential equations”, Computers and mathematics with applications, 62 (2011), 1312–1324 | DOI | MR | Zbl

[33] Zhou Y., Basic theory of fractional differential equations, World Scientific, Singapore, 2010