В настоящей статье, на основе теории топологической степени для уплотняющих многозначных отображений, исследуется существование решений для полулинейных дифференциальных включений дробного порядка $2
диффференциальное включение, дробная производная, антипериодическая краевая задача, функция Грина, мера некомпактности, неподвижная точка, уплотняющий мультиоператор
1. GORENFLO, R, KILBAS, A. A, MAINARDI, F. and ROGOSIN, S. V. (2014) Mittag- Leffler Functions, Related Topics and Applications. Berlin-Heidelberg: Springer- Verlag.
2. HILFER, R. (2000) Applications of Fractional Calculus in Physics. Singapore: World Scientific.
3. KILBAS, A. A., SRIVASTAVA, H. M., and TRUJILLO, J. J. (2006) Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier Science B.V., North-Holland Mathematics Studies.
4. PODLUBNY, I. (1999) Fractional Differential Equations. San Diego: Academic Press.
5. TARASOV, V. E. (2010) Fractional Dynamics. Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. London, New York: Springer.
6. AFANASOVA, M., LIOU, Y. CH., OBUKHOVSKII, V. and PETROSYAN, G. (2019) On Controllability for a System Governed by a Fractional-order Semilinear Functional Differential Inclusion in a Banach Space. Journal of Nonlinear and Convex Analysis. 20 (9). p. 1919-1935.
7. KAMENSKII, M., OBUKHOVSKII, V., PETROSYAN, G., YAO, J. C. (2017) On Semilinear Fractional Order Differential Inclusions in Banach spaces. Fixed Point Theory. 18 (1). p. 269-292.
8. KAMENSKII, M., OBUKHOVSKII, V., PETROSYAN, G., YAO, J. C. (2019) On a Periodic Boundary Value Problem for a Fractional-Order Semilinear Functional Differential Inclusions in a Banach Space. Mathematics. 7 (12). p. 5-19.
9. KAMENSKII, M., OBUKHOVSKII, V., PETROSYAN, G., YAO, J. C. (2021) On the Existence of a Unique Solution for a Class of Fractional Differential Inclusions in a Hilbert Space. Mathematics. 9 (2). p. 136-154.
10. CHEN, Y., NIETO, J. J., O’REGAN, D. (2007) Antiperiodic Solutions for Fully Nonlinear First-order Differential Equations. Math. Comput. Modelling. 46. p. 1183--1190.
11. DELVOS, F.J., KNOCHE, L. (1999) Lacunary Interpolation by Antiperiodic Trigonometric Polynomials. BIT. 39. p. 439--450.
12. SHAO, J. (2008) Anti-periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Time-varying Delays. Phys. Lett. A.. 372. p. 5011--5016.
13. AHMAD, B., NIETO, J. J. (2010) Existence of Solutions for Anti-periodic Boundary Value Problems Involving Fractional Differential Equations via Leray-Schauder Degree Theory. Topological Methods in Nonlinear Analysis. 35. p. 295--304.
14. AGARWAL, R. P., AHMAD, B. (2011) Existence Theory for Anti-periodic Boundary Value Problems of Fractional Differential Equations and Inclusions. Computers and Mathematics with Applications. 62. p. 1200--1214.
15. PETROSYAN, G. (2020) Antiperiodic Boundary Value Problem for a Semilinear Differential Equation of Fractional Order. The Bulletin of Irkutsk State University. series: Mathematics. 34. p. 51-66.
16. KAMENSKII, M., PETROSYAN, G., WEN, C. F (2021) An Existence Result for a Periodic Boundary Value Problem of Fractional Semilinear Differential Equations in a Banach Space. Journal of Nonlinear and Variational Analysis. 5 (1). p. 155-177.
17. KAMENSKII, M., OBUKHOVSKII, V., ZECCA, P. (2001) Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces. Berlin-New-York: Walter de Gruyter.
18. OBUKHOVSKII, V. V, GELMAN, B. D. (2020) Multivalued Maps and Differential Inclusions. Elements of Theory and Applications. Singapore: World Scientific.
19. BOGDAN, V. M. (2010) Generalized Vectorial Lebesgue and Bochner Integration Theory. arXiv:1006.3881v1 [math.FA].
20. DIESTEL, J., RUESS, W. M., SCHACHERMAVER, W. (1993) On weak compactness in L1(μ, X). Proc. Amer. Math. Soc.. 118. p. 447-453.
