We investigate the existence of solutions for a fractional-order boundary-value problem by using some fixed-point theorems. As applications, we present examples illustrating our main results.
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A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, “Theory and applications of fractional differential equations,” North-Holland Math. Stud., 204 (2006).
I. Podlubny, “Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications,” Acad. Press, 198 (1998).
I. Yaslan and M. Gunendi, “Positive solutions of high-order nonlinear multipoint fractional equations with integral boundary conditions,” Fract. Calc. Appl. Anal., 19, No. 4, 989–1009 (2016).
J. Graef, L. Kong, Q. Kong, and M. Wang, “Uniqueness of positive solutions of fractional boundary value problems with nonhomogeneous integral boundary conditions,” Fract. Calc. Appl. Anal., 15, No. 3, 509–528 (2012).
K. Zhang and J. Xu, “Unique positive solution for a fractional boundary value problem,” Fract. Calc. Appl. Anal., 16, No. 4, 937–948 (2013).
M. Dalir and M. Bashour, “Applications of fractional calculus,” Appl. Math. Sci., 4, No. 21, 1021–1032 (2010).
M. ur Rehman and R. A. Khan, “Existence and uniqueness of solutions for multi-point boundary-value problems for fractional differential equations,” Appl. Math. Lett., 23, No. 9, 1038–1044 (2010).
N. Abel, “Solutions de quelques problèmes à l’aide d’intégrales définies,” Euvres complètes de Niels Henrik Abel, 1, 11–18 (1823).
R. P. Agarwal, M. Meehan, and D. O’ Regan, Fixed Point Theory and Applications, Vol. 141, Cambridge Univ. Press (2001).
S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fund. Math., 3, No. 1, 133–181 (1922).
X. Su, “Boundary-value problem for a coupled system of nonlinear fractional differential equations,” Appl. Math. Lett., 22, No. 1, 64–69 (2009).
Y. Guo, “Solvability of boundary-value problems for nonlinear fractional differential equations,” Ukr. Math. Zh., 62, No. 9, 1211–1219 (2010); English translation: Ukr. Math. J., 62, No. 9, 1409–1419 (2011).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 12, pp. 1651–1662, December, 2020. Ukrainian DOI: 10.37863/umzh.v72i12.6033.
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Karaca, I.Y., Oz, D. Existence of Solutions for a Fractional-Order Boundary-Value Problem. Ukr Math J 72, 1907–1920 (2021). https://doi.org/10.1007/s11253-021-01897-z
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DOI: https://doi.org/10.1007/s11253-021-01897-z