Existence of solutions for a fractional-order boundary value problem

I. Y. Karaca; D. Oz

doi:10.37863/umzh.v72i12.6033

I. Y. Karaca Ege Unive., Izmir, Turkey
D. Oz Ege Unive., Izmir, Turkey

DOI: https://doi.org/10.37863/umzh.v72i12.6033

Ключові слова: fractional calculus, boundary value problem, fixed point theorems

Анотація

UDC 517.9

Існування розв’язкiв крайової задачi дробового порядку

За допомогою теорем про нерухому точку вивчено проблему існування розв'язків крайової задачі дробового порядку.
Як застосування наведено приклади, що ілюструють отримані результати.

Посилання

A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North–Holland Mathematics Studies , 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 , Academic press, 198 (1998).

I. Yaslan, M. Gunendi, Positive solutions of high-order nonlinear multi-point fractional equations with integral boundary conditions , Fractional Calculus and Applied Analysis, 19, № 4, 989 – 1009 (2016), https://doi.org/10.1515/fca-2016-0054 DOI: https://doi.org/10.1515/fca-2016-0054

J. Graef, L. Kong, Q. Kong, M. Wang, Uniqueness of positive solutions of fractional boundary value problems withnon-homogeneous integral boundary conditions , Fractional Calculus and Applied Analysis, 15, № 3, 509 – 528 (2012), https://doi.org/10.2478/s13540-012-0036-x DOI: https://doi.org/10.2478/s13540-012-0036-x

K. Zhang, J. Xu, Unique positive solution for a fractional boundary value problem , Fractional Calculus and Applied Analysis, 16, № 4, 937 – 948 (2013), https://doi.org/10.2478/s13540-013-0057-0 DOI: https://doi.org/10.2478/s13540-013-0057-0

M. Dalir, M. Bashour, Applications of fractional calculus , Applied Math. Sciences, 4, № 21-24, 1021 – 1032 (2010).

M. ur Rehman, R. A. Khan, Existence and uniqueness of solutions for multi-point boundary-value problems for fractional differential equations , Applied Mathematics Letters, 23, № 9, 1038 – 1044 (2010), https://doi.org/10.1016/j.aml.2010.04.033 DOI: https://doi.org/10.1016/j.aml.2010.04.033

N. Abel, Solutions de quelques probl`emes `a laide dint´egrales d´efinies , Euvres compl`etes de Niels Henrik Abel, 1, 11 – 18 (1823). DOI: https://doi.org/10.1017/CBO9781139245807.003

R. P. Agarwal, M. Meehan, D. O’ Regan, Fixed point theory and applications , Cambridge University press, 141 (2001), https://doi.org/10.1017/CBO9780511543005 DOI: https://doi.org/10.1017/CBO9780511543005

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. (French) , Fund. Math, 3, № 1, 133 – 181 (1922), https://doi.org/10.4064/fm-3-1-133-181 DOI: https://doi.org/10.4064/fm-3-1-133-181

X. Su, Boundary-value problem for a coupled system of nonlinear fractional differential equations, Applied Mathematics Letters , 22, № 1, 64 – 69 (2009), https://doi.org/10.1016/j.aml.2008.03.001 DOI: https://doi.org/10.1016/j.aml.2008.03.001

Y. Guo, Solvability of boundary-value problems for nonlinear fractional differential equations , Ukr. Math. J., 62, № 9, 1409 – 1419 (2011).