R. Leelavathi1, G. Suresh Kumar2, M.S.N. Murty3 1,2Department of Mathematics
Koneru Lakshmaiah Education Foundation
Vaddeswaram, 522502, Andhra Pradesh, INDIA 3D. No. 21-47, Sainivas, Opp. State Bank of India
Bank Street, Nuzvid, Andhra Pradesh, INDIA
In this paper, we define fuzzy nabla integrals for fuzzy functions on time scales and obtain some of its fundamental properties and also we establish the relationship between nabla differentiation and integration.
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References
[1] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Intro duction with Applications, Birkhauser, Boston (2001).
[2] O.S. Fard, T.A. Bidgoli, Calculus of fuzzy functions on time scales (I), Soft Computing, 19, No 2 (2015), 293-305.
[3] G.S. Guseinov, Integration on time scales, Journal of Mathematical Analysis and Applications 285 (2003), 107-127.
[4] M. Hukahara, Integration des applications measurables dont la valeur est. un compact convexe, Funkcialaj Ekvacioj, 10 (1967), 205-223.
[5] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
[6] V. Lakshmikantham, R.N. Mohapatra, Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis (2003).
[7] R. Leelavathi, G. Suresh Kumar, M.S.N. Murty, Nabla Hukuhara differentiability for fuzzy functions on time scales, Communicated.
[8] R. Leelavathi, G. Suresh Kumar, M.S.N. Murty, Second type Nabla Hukuhara differentiability for fuzzy functions on time scales, Communicated.
[9] C.H. Vasavi, G. Suresh Kumar, M.S.N. Murty, Fuzzy Hukahara delta differential and applications to fuzzy dynamic equations on time scales, Journal of Uncertain Systems, 10, No 1 (2016), 163-180.
[10] C.H. Vasavi, G. Suresh Kumar, M.S.N. Murty, Fuzzy dynamic equations on time scales under second type Hukuhara delta derivative, International Journal of Chemical Sciences, 14, No 1 ( 2016), 49-66.
[11] C.H. Vasavi, G. Suresh Kumar, M.S.N. Murty, Generalized differentiability and integrability for fuzzy set-valued functions on time scales, Soft Computing, 20 (2016), 1093-1104.