Research article

Oscillation results for a fractional partial differential system with damping and forcing terms

  • Received: 11 September 2022 Revised: 11 November 2022 Accepted: 24 November 2022 Published: 02 December 2022
  • MSC : 34C10, 34K11, 35B05, 35R11

  • In this paper, we study the forced oscillation of solutions of a fractional partial differential system with damping terms by using the Riemann-Liouville derivative and integral. We obtained some new oscillation results by using the integral averaging technique. The obtained results are illustrated by using some examples.

    Citation: A. Palanisamy, J. Alzabut, V. Muthulakshmi, S. S. Santra, K. Nonlaopon. Oscillation results for a fractional partial differential system with damping and forcing terms[J]. AIMS Mathematics, 2023, 8(2): 4261-4279. doi: 10.3934/math.2023212

    Related Papers:

  • In this paper, we study the forced oscillation of solutions of a fractional partial differential system with damping terms by using the Riemann-Liouville derivative and integral. We obtained some new oscillation results by using the integral averaging technique. The obtained results are illustrated by using some examples.



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    [1] S. Abbas, M. Benchohra, G. M. N'Guérékata, Topics in fractional differential equations, New York: Springer, 2012.
    [2] V. P. Dubey, R. Kumar, J. Singh, D. Kumar, An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves, J. Ocean Eng. Sci., 6 (2021), 30–39. https://doi.org/10.1016/j.joes.2020.04.006 doi: 10.1016/j.joes.2020.04.006
    [3] J. Alzabut, A. G. Selvam, R. Dhineshbabu, M. K. A. Kaabar, The existence, uniqueness, and stability analysis of the discrete fractional three-point boundary value problem for the elastic beam equation, Symmetry, 13 (2021), 1–18. https://doi.org/10.3390/sym13050789 doi: 10.3390/sym13050789
    [4] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science Publishers BV, Amsterdam, 2006.
    [5] R. Courant, D. Hilbert, Methods of mathematical physics, Interscience, New York, 1966.
    [6] K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley and Sons, New York, 1993.
    [7] I. Podlubny, Fractional differential equations, New York: Academic Press, 1998.
    [8] M. Iswarya, R. Raja, G. Rajchakit, J. Cao, J. Alzabut, C. Huang, A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with time-varying delays, Adv. Differ. Equ., 502 (2019), 502. https://doi.org/10.1186/s13662-019-2443-3 doi: 10.1186/s13662-019-2443-3
    [9] M. Sambath, P. Ramesh, K. Balachandran, Asymptotic behavior of the fractional order three species prey-predator model, Int. J. Nonlinear Sci. Numer. Simul., 19 (2018), 721–733. https://doi.org/10.1515/ijnsns-2017-0273 doi: 10.1515/ijnsns-2017-0273
    [10] Y. Zhou, Fractional evolution equations and inclusions: analysis and control, New York: Elsevier, 2015.
    [11] R. P. Agarwal, M. Bohner, T. Li, Oscillatory behavior of second-order half-linear damped dynamic equations, Appl. Math. Comput., 254 (2015), 408–418. https://doi.org/10.1016/j.amc.2014.12.091 doi: 10.1016/j.amc.2014.12.091
    [12] J. Alzabut, R. P. Agarwal, S. R. Grace, J. M. Jonnalagadda, Oscillation results for solutions of fractional-order differential equations, Fractal Fract., 6 (2022), 466. https://doi.org/10.3390/fractalfract6090466 doi: 10.3390/fractalfract6090466
    [13] M. Bohner, T. Li, Kamenev-type criteria for nonlinear damped dynamic equations, Sci. China Math., 58 (2015), 1445–1452. https://doi.org/10.1007/s11425-015-4974-8 doi: 10.1007/s11425-015-4974-8
    [14] K. S. Chiu, T. Li, Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments, Math. Nachr., 292 (2020), 2153–2164. https://doi.org/10.1002/mana.201800053 doi: 10.1002/mana.201800053
    [15] J. Džurina, S. R. Grace, I. Jadlovská, T. Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293 (2020), 910–922. https://doi.org/10.1002/mana.201800196 doi: 10.1002/mana.201800196
    [16] T. Li, Y. V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), 1–7. https://doi.org/10.1016/j.aml.2020.106293 doi: 10.1016/j.aml.2020.106293
    [17] J. Alzabut, R. P. Agarwal, S. R. Grace, J. M. Jonnalagadda, A. G. M Selvam, C. Wang, A survey on the oscillation of solutions for fractional difference equations, Mathematics, 10 (2022), 894. https://doi.org/10.3390/math10060894 doi: 10.3390/math10060894
    [18] T. Li, N. Pintus, G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (2019), 1–18. https://doi.org/10.1007/s00033-019-1130-2 doi: 10.1007/s00033-019-1130-2
    [19] T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differ. Integral Equ., 34 (2021), 315–336.
    [20] S. Harikrishnan, P. Prakash, J. J. Nieto, Forced oscillation of solutions of a nonlinear fractional partial differential equation, Appl. Math. Comput., 254 (2015), 14–19. https://doi.org/10.1016/j.amc.2014.12.074 doi: 10.1016/j.amc.2014.12.074
    [21] H. Kong, R. Xu, Forced oscillation of fractional partial differential equations with damping term, Fract. Differ. Calc., 7 (2017), 325–338.
    [22] W. N. Li, On the forced oscillation of certain fractional partial differential equations, Appl. Math. Lett., 50 (2015), 5–9. https://doi.org/10.1016/j.aml.2015.05.016 doi: 10.1016/j.aml.2015.05.016
    [23] W. N. Li, W. Sheng, Oscillation properties for solution of a kind of partial fractional differential equations with damping term, J. Nonlinear Sci. Appl., 9 (2016), 1600–1608.
    [24] L. Luo, Z. Luo, Y. Zeng, New results for oscillation of fractional partial differential equations with damping term, Discrete Cont. Dyn. Syst. Ser. S, 14 (2021), 3223–3231.
    [25] D. Xu, F. Meng, Oscillation criteria of certain fractional partial differential equations, Adv. Differ. Equ., 2019 (2019), 1–12. https://doi.org/10.1186/s13662-019-2391-y doi: 10.1186/s13662-019-2391-y
    [26] P. Prakash, S. Harikrishnan, J. J. Nieto, J. H. Kim, Oscillation of a time fractional partial differential equation, Electron. J. Qual. Theory Differ. Equ., 15 (2014), 1–10.
    [27] Q. Ma, K. Liu, A. Liu, Forced oscillation of fractional partial differential equations with damping term, J. Math., 39 (2019), 111–120.
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