By using the Krasnoselskii theorem, we obtain general conditions for the unique solvability of boundaryvalue problems for (non)linear fractional functional-differential equations.
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A. Aphithana, S. K. Ntouyas, and J. Tariboon, “Existence and uniqueness of symmetric solutions for fractional differential equations with multi-order fractional integral conditions,” Bound. Value Probl., 68, (2015); https://doi.org/10.1186/s13661-015-0329-1.
K. Diethelm, The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type, Lect. Notes Math., Springer-Verlag, Berlin (2010).
M. Feˇckan, J. R. Wang, and M. Pospíšil, Fractional-Order Equations and Inclusions, Fractional Calculus in Applied Sciences and Engineering, 3, de Gruyter, Berlin (2017).
M. Feˇckan and K. Marynets, “Approximation approach to periodic BVP for fractional differential systems,” Eur. Phys. J. Spec. Topics, 226, 3681–3692 (2017).
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Amsterdam (2006).
D. C. Labora and R. Rodríguez–López, “From fractional order equations to integer order equations,” Fract. Calc. Appl. Anal., 20, No. 6, 1405–1423 (2017).
V. Lakshmikantham, “Theory of fractional functional differential equations,” Nonlin. Anal., 69, No. 10, 15, 3337–3343 (2008).
E. I. Bravyi, “On periods of non-constant solutions to functional differential equations,” Electron. J. Qual. Theory Differ. Equat., Paper No. 14 (2017).
Z. Opluštil and J. Šremr, “On a non-local boundary value problem for linear functional differential equations,” Electron. J. Qual. Theory Differ. Equat., 2009, Paper No. 36 (2009).
A. Rontó, M. Rontó, and N. Shchobak, “On boundary value problems with prescribed number of zeroes of solutions,” Miskolc Math. Notes, 18, No. 1, 431–452 (2017).
A. Rontó and M. Rontó, “Successive approximation techniques in non-linear boundary value problems for ordinary differential equations,” in: Handbook of Differential Equations: Ordinary Differential Equations, Vol. IV, Elsevier/North-Holland, Amsterdam (2008), pp. 441–592.
N. Dilna and M. Fečkan, “The Stieltjes string model with external load,” Appl. Math. Comput., 337, 350–359 (2018).
N. Dilna, M. Fečkan, and A. Rontó, “On a class of functional differential equations with symmetries,” Symmetry, 11, No. 12, 1456 (2019); DOI: https://doi.org/10.3390/sym11121456.
N. Dilna, “On non-local boundary-value problems for higher-order non-linear functional differential equations,” in: S. Pinelas, J. R. Graef, S. Hilger, P. Kloeden, and C. Schinas (editors), Differential and Difference Equations with Applications, Springer, Cham, 333 (2020), pp. 535–548.
N. Dilna, M. Fečkan, and M. Solovyov, “D-Stability of the initial value problem for symmetric nonlinear functional differential equations,” Symmetry, 12, No. 11, 1761 (2020); 10.3390/sym12111761.
N. Azbelev, V. Maksimov, and L. Rakhmatullina, Introduction to the Theory of Linear Functional-Differential Equations, Advanced Series in Mathematical Science and Engineering, 3, World Federation Publ. Comp., Atlanta, GA (1995).
M. A. Krasnoselskii and P. P. Zabreiko, Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin (1984).
M. A. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff, Groningen (1964).
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The present paper is dedicated to Prof. Michal Fečkan on the occasion of his 60th birthday
Published in Neliniini Kolyvannya, Vol. 24, No. 1, pp. 17–27, January–March, 2021.
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Dilna, N., Gromyak, M. & Leshchuk, S. Unique Solvability of the Boundary-Value Problems for Nonlinear Fractional Functional Differential Equations. J Math Sci 265, 577–588 (2022). https://doi.org/10.1007/s10958-022-06072-8
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DOI: https://doi.org/10.1007/s10958-022-06072-8