Geodesic
Existence of solutions to multi-point boundary value problem of fractional order on the half-line
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2023), pp. 37-56 
Abdellatif Ghendir Aoun. Existence of solutions to multi-point boundary value problem of fractional order on the half-line. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2023), pp. 37-56. http://geodesic.mathdoc.fr/item/BASM_2023_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The purpose of this paper is to establish the existence of solutions to multi-point fractional boundary value problem on an infinite interval. Using the fixed point theory, sufficient conditions are obtained that guarantee the existence of at least one solution. At the end, an example is presented to illustrate the main results

[1] Agarwal Ravi P., Meehan Maria, O'Regan Donal, Fixed point theory and applications, Cambridge Tracts in Mathematics, 141, Cambridge University Press, Cambridge, 2001 | MR | Zbl

[2] Z. Bai and Y. Zhang, “The existence of solutions for a fractional multi-point boundary value problem”, Comput. Math. Appl., 60 (2010), 2364–2372 | DOI | MR | Zbl

[3] Y. Gholami, “Existence of an unbouded solution for multi-point boundary value problems of fractional differential equations on an infinite domain, class of Riemann-Liouville fractional differential equations”, FDC, 4:2 (2014), 125–136 | MR | Zbl

[4] K. Ghanbari, Y. Gholami, “Existence and multiplicity of positive solutions for m-point nonlinear fractional differential equations on the half-line”, EJDE, 2012:238 (2012), 1–15 | MR | Zbl

[5] A. Ghendir Aoun, “On a three-point fractional integral boundary value problem on the half-line”, JNFA, 2019, 16, 18 pp.

[6] J. He, X. Zhang, L. Liu, Y. Wu, Y. Gui, “Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions”, Boundary Value Problems, 2018 (2018), 189 | DOI | MR

[7] R. A. Khan and H. Khan, “On existence of solution for multi-points boundary value problem”, JFCA, 5 (2014), 121–132 | MR | Zbl

[8] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B. V., Amsterdam, 2006 | MR | Zbl

[9] B. Li, S. Sun, Y. Li and P. Zhao, “Multi-point boundary value problems for a class of Riemann-Liouville fractional differential equations”, Advances in Difference Equations, 2014 (2014), 151 | DOI | MR

[10] S. Liang and J. Zhang, “Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval”, Mathematical and Computer Modelling, 54 (2011), 1334–1346 | DOI | MR | Zbl

[11] K. Oldham and J. Spanier, The fractional calculus. Theory and applications of differentiation and integration to arbitrary order, 1974, 240 pp. | MR | Zbl

[12] X. Su and S. Zhang, “Unbounded solutions to a boundary value problem of fractional order on the half-line”, Computers and Mathematics with Applications, 61 (2011), 1079–1087 | DOI | MR | Zbl

[13] C. Shen, H. Zhou and L. Yang, “On the existence of solution to a boundary value problem of fractional differential equation on the infinite interval”, Boundary Value Problems, 2015 (2015), 241 | DOI | MR

[14] G. Wang, “Explicit iteration and unbounded solutions for fractional integral boundary value problem on an infinite interval”, Applied Mathematics Letters, 47 (2015), 1–7 | DOI | MR | Zbl

[15] C. Yu, J. Wang and Y. Guo, “Solvability for integral boundary value problems of fractional differential equation on infinite intervals”, J. Nonlinear Sci. Appl., 9 (2016), 160–170 | DOI | MR | Zbl

[16] X. Zhao, W. Ge, “Unbounded solutions for a fractional boundary value problem on the infinite interval”, Acta. Appl. Math., 109 (2010), 495–505 | DOI | MR | Zbl