Averaging of fuzzy differential equations on a finite interval

L. Zadeh, “Fuzzy sets,” Inf. Control, No. 8, 338–353 (1965).

M. L. Puri and D. A. Ralescu, “Differentials of fuzzy functions,” J. Math. Anal. Appl., 91, 552–558 (1983).

M. Hukuhara, “Intégration des applications mesurables dont la valeur est un compact convexe,” Funkc. Ekvac., No. 10, 205–223 (1967).

R. J. Aumann, “Integrals of set-valued functions,” J. Math. Anal. Appl., No. 12, 1–12 (1965).

O. Kaleva, “Fuzzy differential equations,” Fuzzy Sets Syst., 24, No. 3, 301–317 (1987).

O. Kaleva, “The Cauchy problem for fuzzy differential equations,” Fuzzy Sets Syst., No. 35, 389–396 (1990).

O. Kaleva, “The Peano theorem for fuzzy differential equations revisited,” Fuzzy Sets Syst., No. 98, 147–148 (1998).

O. Kaleva, “A note on fuzzy differential equations,” Nonlin. Anal., No. 64, 895–900 (2006).

V. Lakshmikantham, T. G. Bhaskar, and J. Vasundhara Devi, Theory of Set Differential Equations in Metric Spaces, Cambridge Scientific, Cambridge (2006).

V. Lakshmikantham and R. N. Mohapatra, Theory of Fuzzy Differential Equations and Inclusions, Florida Institute of Technology, Melbourne (2003).

J.Y. Park and H. K. Han, “Existence and uniqueness theorem for a solution of fuzzy differential equations,” Int. J. Math. Math. Sci., 22, No. 2, 271–279 (1999).

J.Y. Park and H. K. Han, “Fuzzy differential equations,” Fuzzy Sets Syst., No. 110, 69–77 (2000).

D. Vorobiev and S. Seikkala, “Towards the theory of fuzzy differential equations,” Fuzzy Sets Syst., No. 125, 231–237 (2002).

S. Seikkala, “On the fuzzy initial value problem,” Fuzzy Sets Syst., No. 24, 319–330 (1987).

T. A. Komleva, A. V. Plotnikov, and N. V. Skripnik, “Ω-space and its relation to the theory of fuzzy sets,” Tr. Odes. Politekhn. Inst., Issue 2(28), 182–191 (2007).

T. A. Komleva, A. V. Plotnikov, and N. V. Skripnik, “Differential equations with set-valued solutions,” Ukr. Mat. Zh., 60, No. 10, 1326–1337 (2008); English translation: Ukr. Math. J., 60, No. 10, 1540–1556 (2008).

N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).

N. M. Krylov and N. N. Bogolyubov, Introduction to Nonlinear Mechanics, Ukrainian Academy of Sciences, Kiev (1937).

Yu. A. Mitropol’skii, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).

Yu. A. Mitropol’skii and G. N. Khoma, Mathematical Justification of Asymptotic Methods of Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1983).

N. A. Perestyuk, V. A. Plotnikov, A. M. Samoilenko, and N. V. Skripnik, Impulsive Differential Equations with Set-Valued and Discontinuous Right-Hand Sides [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2007).

V. A. Plotnikov, Asymptotic Methods in Problems of Optimal Control [in Russian], Odessa State University, Odessa (1976).

V. A. Plotnikov, “Averaging of differential inclusions,” Ukr. Mat. Zh., 31, No. 5, 573–576 (1979); English translation: Ukr. Math. J., 31, No. 5, 454–457 (1979).

V. A. Plotnikov, A. V. Plotnikov, and A. N. Vityuk, Differential Equations with Set-Valued Right-Hand Sides. Asymptotic Methods [in Russian], AstroPrint, Odessa (1999).

A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).

A. M. Samoilenko and Yu. V. Teplinskii, Countable Systems of Differential Equations [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1993).

M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” J. Math. Anal. Appl., No. 114, 409–422 (1986).

M. Stojaković, “R n -valued fuzzy random variable,” Univ. Novom Sadu Zb. Rad. Prirod. Mat. Fak., Ser. Mat., 20, No. 2, 95–103 (1990).

M. Kisielewicz, “Method of averaging for differential equations with compact convex valued solutions,” Rend. Math., 9, No. 3, 397–408 (1976).

A. N. Filatov and L. V. Sharova, Integral Inequalities and Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1976).

M. M. Khapaev, “On the averaging method and some problems related to averaging,” Differents. Uravn., 11, No. 5, 600–608 (1966).