Lyapunov-type inequality for higher order left and right fractional p-Laplacian problems

  1. Cabada, Alberto
  2. Khaldi, Rabah 1
  1. 1 Badji Mokhtar Annaba University.
Zeitschrift:
Proyecciones: Journal of Mathematics

ISSN: 0716-0917,  0717-6279

Datum der Publikation: 2021

Ausgabe: 40

Nummer: 4

Seiten: 1031-1040

Art: Artikel

DOI: 10.22199/ISSN.0717-6279-4366 DIALNET GOOGLE SCHOLAR lock_openOpen Access editor

Andere Publikationen in: Proyecciones: Journal of Mathematics

Ziele für nachhaltige Entwicklung

Zusammenfassung

In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, we apply the Schaefer’s fixed point theorem. Furthermore, we present the Lyapunov inequality for the corresponding problem.

Bibliographische Referenzen

  • B. Ahmad, S.K. Ntouyas, and A. Alsaedi, “Existence theory for nonlocal boundary value problems involving mixed fractional derivatives”, Nonlinear analysis: modelling and control, vol. 24, no. 6, pp. 937-957, 2019. https://doi.org/10.15388/NA.2019.6.6
  • B. Ahmad, A. Broom, A. Alsaedi, and S. K. Ntouyas, “Nonlinear integro-differential equations involving mixed right and left fractional derivatives and integrals with nonlocal boundary data”, Mathematics, vol. 8, no. 3, Art ID. 336, 2020. https://doi.org/10.3390/math8030336
  • B. Ahmad, S. K. Ntouyas, and A. Alsaedi, “Fractional order differential systems involving right Caputo and left Riemann–Liouville fractional derivatives with nonlocal coupled conditions”, Boundary value problems, vol. 2019, no. 1, Art ID. 109, 2019. https://doi.org/10.1186/s13661-019-1222-0
  • R. Almeida, S. Pooseh, and D. F. M. Torres, Computational Methods in the Fractional Calculus of Variations. London: Imperial College Press, 2015. https://doi.org/10.1142/p991
  • A. Alsaedi, A. Broom, S. K. Ntouyas, and B. Ahmad, “Nonlocal fractional boundary value problems involving mixed right and left fractional derivatives and integrals”, Axioms, vol. 9, no. 2, Art ID. 50, 2020, https://doi.org/10.3390/axioms9020050
  • A. Guezane-Lakoud, R. Khaldi, and A. Kılıçman, “Existence of solutions for a mixed fractional boundary value problem”, Advances in difference equations, Art. ID. 164 2017. https://doi.org/10.1186/s13662-017-1226-y
  • A. Guezane-Lakoud, R. Khaldi, and D. F.M. Torres, “Lyapunov-type inequality for a fractional boundary value problem with natural conditions”, SeMA journal, vol. 75, pp. 157-162, 2018, https://doi.org/10.1007/s40324-017-0124-2
  • A. Guezane-Lakoud, R. Khaldi, and D. F. M. Torres, “On a fractional oscillator equation with natural boundary conditions”, Progress in fractional differentiation and applications, vol. 3, no. 3, pp. 191-197, 2017, https://doi.org/10.18576/pfda/030302
  • R. Khaldi and A Guezane-Lakoud, “On a generalized Lyapunov inequality for a mixed fractional boundary value problem”, AIMS mathematics, vol. 4, no. 3, pp. 506-515, 2019, https://doi.org/10.3934/math.2019.3.506
  • R. Khaldi and A Guezane-Lakoud, “Lyapunov inequality for a boundary value problem involving conformable derivative”, Progress in fractional differentiation and applications, vol. 4, no. 4, pp. 323-329, https://doi.org/10.18576/pfda/030407
  • R. Khaldi and A. Guezane-Lakoud, “Higher order fractional boundary value problems for mixed type derivatives”, Journal of nonlinear functional analysis, vol. 2017, Art. ID 30, 2017, https://doi.org/10.23952/jnfa.2017.30
  • A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equation. Amsterdam: Elsevier Science, 2006.
  • A. B. Malinowska, T. Odzijewicz, and D. F. M. Torres, Advanced methods in the fractional calculus of variations. Cham: Springer, 2015, https://doi.org/10.1007/978-3-319-14756-7
  • A. B. Malinowska and D. F. M. Torres, “Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative”, Computers & mathematics with applications, vol. 59, no. 9, pp. 3110-3116, 2010, https://doi.org/10.1016/j.camwa.2010.02.032
  • I. Merzoug, A. Guezane-Lakoud, and R. Khaldi, “Existence of solutions for a nonlinear fractional p-Laplacian boundary value problem”, Rendiconti del Circolo Matematico di Palermo Series 2, vol. 69, 2019, https://doi.org/10.1007/s12215-019-00459-4
  • S. K. Ntouyas, B. A. Ahmad, and T. P. Horikis, “Recent developments of Lyapunov–type inequalities for fractional differential equations”, in Differential and integral inequalities, D. Andrica and T. Rassias, Eds. Cham: Springer, 2019, pp. 619–686, https://doi.org/10.1007/978-3-030-27407-8_24
  • I. Podlubny, Fractional differential equations. San Diego, CA: Academic Press, 1999.
  • S. G. Samko, O. I. Marichev, and A. A. Kilbas, Fractional integrals and derivatives: theory and applications. Amsterdam: Gordon and Breach Science Publishers, 1993 [Online]. Available: https://bit.ly/2WNwdlk
Fuente de los datos: Dialnet