Document Type : Research Paper


1 Odessa State Academy of Civil Engineering and Architecture, Odessa, Ukraine

2 Odessa National Polytechnic University, Odessa, Ukraine


In this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist. 


[1] Agarval R. P., O'Regan D., Lakshmikantham V., Maximal solutions and existence theory for fuzzy differential and integral equations. J. of Applied Analysis, 11 (2), 171-186, 2005.
[2] Aubin J. P., Fuzzy differential inclusions. Probl. Control Inf. Theory, 19 (1), 55-67, 1990.
[3] Aubin J. P., Cellina A., Differential Inclusions. (Springer Verlag, New York, 1984).
[4] Aumann R. J., Integrals of set-valued functions. J. Math. Anal. Appl., 12, 1-12, 1965.
[5] Baidosov V. A., Differential inclusions with fuzzy right-hand side. Soviet Mathematics, 40 (3), 567-569, 1990.
[6] Baidosov V. A., Fuzzy differential inclusions. J. of Appl. Math. And Mechan., 54 (1), 8-13, 1990.
[7] Filippov A. F., Classical solutions of differential equations with multi-valued right-hand side. SIAM J. Control. 5, 609-621, 1967.
[8] Hullermeier E., An approach to modelling and simulation of uncertain dynamical system. Internat. J. Uncertain. Fuzziness Knowledge - Based Systems, 7, 117-137, 1997.
[9] Komleva T. A., Plotnikov A. V., Plotnikova L. I., Averaging of differential inclusions with fuzzy right-hand side of the closed interval . Work of the Odessa Polytehnikal University. 33 (1)-34 (2), 192-196, 2010.
[10] Kuratowski K., Topology. Vol. 1 (Academic Press, New York and London, 1966).
[11] Lakshmikantham V., Mohapatra R., Theory of fuzzy differential equations anf inclusions (Taylor - Francis, 2003).
[12] Marchaud A., Sur les champs de demicones et equations differentielles du premier order. Bull. Soc. Math. France, 62, 1-38, 1934.
[13] Marchaund A., Sur les champs des deme-droites et les equations differentilles du premier ordre. Bull. Soc. Math. France, 63, 1-38, 1934.
[14] Park J. Y., Han H. K., Existence and uniqueness theorem for a solution of fuzzy differential equations. Internat. J. Math. and Math. Sci., 22 (2), 271-279, 1999.
[15] Plotnikov V. A., Plotnikov A. V., Vityuk A. N.,  Differential equations with a multivalued right-hand side: Asymptotic methods (Astroprint, Odessa, 1999).
[16] Puri M. L., Ralescu D. A., Differentielle d'une fonction floue. C.R. Acad. Sc. Paris, 293 (1), 237-239, 1981.
[17] Puri M. L., Ralescu D. A., Fuzzy random variables. J. Math. Anal. Appl., 114 (2), 409-422, 1986.
[18] Wazewski T., Systemes de commande et equations au contingent. Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys., 9, 151-155, 1961.
[19] Zaremba S. C., Sur une extension de la notion d'equation differentielle. Comptes rendus Acad. Sc., Paris, 199, 1278-1280, 1934.