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On semidiscretization methods for differential inclusions of fractional order

Annotation

The report provides semidiscretization diagram for semilinear differential inclusions of fractional order.

Keywords

fractional differential inclusion; semilinear differential inclusion; Cauchy problem; approximation; semidiscretization; fixed point; condensing map; measure of noncompactness

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DOI

10.20310/1810-0198-2018-23-122-125-130

UDC

517.92

Pages

125-130

References

1. Akhmerov R.R., Kamenskiy M.I., Potapov A.S., Rodkina A.E., Sadovskiy B.N. Mery nekompaktnosti i uplotnyayushchie operatory [Measures of Non-Compactness and Condensing Operators]. Novosibirsk, Nauka Publ., 1986. (In Russian). 2. Borisovich Yu.G., Gelman B.D., Myshkis A.D., Obukhovskiy V.V. Vvedenie v teoriyu mnogoznachnykh otobrazheniy i differentsial'nykh vklyucheniy [Introduction to the Theory of Many-Valued Separations and Differential Inclusions]. Moscow, Book House “Librokom” Publ., 2011. (In Russian). 3. Kamenskii M., Obukhovskii V., Petrosyan G., Yao J.-C. On semilinear fractional order differential inclusions in banach spaces. Fixed Point Theory, 2017, vol. 18, no. 1, pp. 269-292. 4. Kamenskii M., Obukhovskii V., Petrosyan G., Yao J.-C. Boundary value problems for semilinear differential inclusions of fractional order in a Banach space. Applicable Analysis, 2017, vol. 96, pp. 1-21. 5. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Applications of Fractional Differential Equations. Amsterdam, Elsevier Science, 2006, 541 p. 6. Petrosyan G.G., Afanasova M.S. O zadache koshi dlya differentsial'nogo vklyucheniya drobnogo poryadka s nelineynym granichnym usloviem [On the Cauchy problem for a differential inclusion of fractional order with nonlinear boundary conditions]. Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika – Proceedings of Voronezh State University. Series: Physics. Mathematics, 2017, no. 1, pp. 135-151. (In Russian). 7. Petrosyan G.G. On the structure of the solutions set of the Cauchy problem for a differential inclusions of fractional order in a Banach space. Nekotorye voprosy analiza, algebry, geometrii i matematicheskogo obrazovaniya [Some Questions of Analysis, Algebra, Geometry and Mathematical Education]. Voronezh, 2016, pp. 7-8.

Received

2018-03-21

Section of issue

Scientific articles

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