The monotone iterative method for the integral boundary value problems of fractional p-Laplacian equations with delay

References

[1] Y. Wei, Q. Song, Z. Bai, “Existence and iterative method for some fourth order nonlinear boundary value problems,” Appl. Math. Lett., vol. 87, pp. 101–107, 2019. https://doi.org/10.1016/j.aml.2018.07.032.Search in Google Scholar

[2] M. Jia, X. Liu, “Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions,” Appl. Math. Comput., vol. 232, pp. 313–323, 2014. https://doi.org/10.1016/j.amc.2014.01.073.Search in Google Scholar

[3] Z. Han, H. Lu, C. Zhang, “Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian,” Appl. Math. Comput., vol. 257, pp. 526–536, 2015. https://doi.org/10.1016/j.amc.2015.01.013.Search in Google Scholar

[4] X. Liu, M. Jia, “Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives,” Appl. Math. Comput., vol. 353, pp. 230–242, 2019. https://doi.org/10.1016/j.amc.2019.02.011.Search in Google Scholar

[5] M. U. Rehman, R. A. Khan, “Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations,” Appl. Math. Lett., vol. 23, no. 9, pp. 1038–1044, 2010.10.1016/j.aml.2010.04.033Search in Google Scholar

[6] Q. Song, Z. Bai, “Positive solutions of fractional differential equations involving the Riemann-Stieltjes integral boundary condition,” Adv. Differ. Equ., vol. 2018, no. 183, pp. 1–7, 2018. https://doi.org/10.1186/s13662-018-1633-8.Search in Google Scholar

[7] B. Ahmad, Y. Alruwaily, A. Alsaedi, S. K. Ntouyas, “Existence and stability results for a fractional order differential equation with non-conjugate Riemann–Stieltjes integro-multipoint boundary conditions,” Mathematics, vol. 7, no. 3, pp. 1–14, 2019. https://doi.org/10.3390/math7030249.Search in Google Scholar

[8] B. Ahmad, M. Alghanmi, S. K. Ntouyas, A. Alsaedi, “Fractional differential equations involving generalized derivativewith Stieltjes and fractional integral boundary conditions,” Appl. Math. Lett., vol. 84, pp. 111–117, 2018. https://doi.org/10.1016/j.aml.2018.04.024.Search in Google Scholar

[9] T. Lv, H. Pang, L. Cao, “Existence results for fractional differential equations with multistrip Riemann–Stieltjes integral boundary conditions,” Discrete Dyn. Nat. Soc., vol. 2018, pp. 1–8, 2018. https://doi.org/10.1155/2018/2352789.Search in Google Scholar

[10] X. Liu, M. Jia, “The method of lower and upper solutions for the general boundary value problems of fractional differential equations with p-Laplacian,” Adv. Differ. Equ., vol. 2018, no. 28, pp. 1–15, 2018. https://doi.org/10.1186/s13662-017-1446-1.Search in Google Scholar

[11] X. Liu, M. Jia, W. Ge, “The method of lower and upper solutions for mixed fractional four-point boundary value problem with p-Laplacian operator,” Appl. Math. Lett., vol. 65, pp. 56–62, 2017. https://doi org/10.1016/j.aml.2016.10.001.10.1016/j.aml.2016.10.001Search in Google Scholar

[12] B. Khamessi, A. Hamiaz, “Existence and exact asymptotic behaviour of positive solutions for fractional boundary value problem with p-Laplacian operator,” J. Taibah Univ. Sci., vol. 13, no. 1, pp. 370–376, 2019. https://doi.org/10.1080/16583655.2019.1579953.Search in Google Scholar

[13] K. Jong, H. Choi, Y. Ri, “Existence of positive solutions of a class of multi-point boundary value problems for p-Laplacian fractional differential equations with singular source terms,” Commun. Nonlinear Sci. Numer. Simul., vol. 72, pp. 272–281, 2019. https://doi.org/10.1016/j.cnsns.2018.12.021.Search in Google Scholar

[14] K. B. Lee, J. R. Howell, “Theoretical and experimental heat and mass transfer in highly porous media,” Int. J. Heat Mass Transfer, vol. 34, no. 8, pp. 2123–2132, 1991. https://doi org/10.1016/0017-9310(91)90222-Z.10.1016/0017-9310(91)90222-ZSearch in Google Scholar

[15] S. Lu, L. Niu, Y. Guo, L. Chen, “Existence of positive periodic solutions for neutral Liénard equations with a singularity of repulsive type,” Math. Appl., vol. 31, no. 3, pp. 481–489, 2018. https://doi org/10.13642/j.cnki.42-1184/o1.2018.03.029.10.1007/s11784-019-0669-zSearch in Google Scholar

[16] S. Lu, X. Yu, “Existence of positive periodic solutions for a neutral Liénard equation with a singularity of repulsive type,” J. Fixed Point Theory Appl., vol. 21, no. 1, pp. 1–15, 2019. https://doi.org/10.1007/s11784-019-0669-z.Search in Google Scholar

[17] X. Su, “Positive solutions to singular boundary value problems for fractional function differential equations with changing sign nonlinearity,” Comput. Math. Appl., vol. 64, no. 10, pp. 3425–3435, 2012. https://doi.org/10.1016/j.camwa.2012.02.043.Search in Google Scholar

[18] Y. Zhang, Z. Zhou, “Positive solutions for fourth-order delay differential equation of boundary value problem with p-Laplacian,” Chin. Quart. J. Math., vol. 29, no. 2, pp. 171–179, 2014. https://doi org/10.13642/j.cnki.42-1184/o1.2018.03.02.Search in Google Scholar

[19] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam, The Netherlands, Elsevier Science Ltd, 2006.Search in Google Scholar

[20] D. Guo, J. Sun, Z. Liu, Nonlinear Ordinary Differential Equation Function Method, Jinan, China, Shandong Science and Technology Press, 2006 (in Chinese).Search in Google Scholar

[21] I. Podlubny, Fractional Differential Equations, San Diego, Academic Press, 1999.Search in Google Scholar