تعداد نشریات | 26 |
تعداد شمارهها | 550 |
تعداد مقالات | 5,700 |
تعداد مشاهده مقاله | 7,968,647 |
تعداد دریافت فایل اصل مقاله | 5,350,935 |
First order linear fuzzy dynamic equations on time scales | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 15، دوره 16، شماره 2، خرداد و تیر 2019، صفحه 183-196 اصل مقاله (245.34 K) | ||
نوع مقاله: Original Manuscript | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2019.4551 | ||
نویسندگان | ||
Alireza Khastan ![]() | ||
1Department of Mathematics Institute for Advanced Studies in Basic Sciences | ||
2Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran. | ||
چکیده | ||
In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Using the derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. We present some examples to illustrate our results. | ||
کلیدواژهها | ||
Time scales؛ Generalized differentiability؛ First order؛ Linear fuzzy dynamic equations | ||
مراجع | ||
[1] O. Abu Arqub, M. AL-Smadi, S. Momani, T. Hayat, Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method, Soft Computing, 20 (2016), 3283–3302. [2] O. Abu Arqub, M. AL-Smadi, S. Momani, T. Hayat, Application of reproducing kernel algorithm for solving secondorder two-point fuzzy boundary value problems, Soft Computing, 21 (2017), 7191–7206. [3] O. Abu Arqub, Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations, Neural Computing & Applications, 28 (2017), 1591–1610. [4] R.P. Agarwal, Difference Equations and Inequalities: Theory, Methods, and Applications, Marcel Dekker, New York, 1992. [5] S.E. Amrahov, A. Khastan, N. Gasilov, A.G. Fatullayev, Relationship between Bede{Gal differentiable set-valued functions and their associated support functions, Fuzzy Sets and Systems, 295 (2016), 57–71 [6] B. Bede, S.G. Gal, Generalizations of the differentiability of fuzzy number value functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151 (2005), 581–599. [7] B. Bede, I. J. Rudas, A. L. Bencsik, First order linear fuzzy differential equations under generalized differentiability, Information Sciences, 177 (2007), 1648–1662. [8] B. Bede, Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, London, 2013. [9] M. Bohner, A. Peterson, Dynamic equations on time scales: An introduction with applications, Springer Science & Business Media, 2012. [10] K. A. Chrysafis, B. K. Papadopoulos, G. Papaschinopoulos, On the fuzzy difference equations of finance, Fuzzy Sets and Systems, 159 (2008), 3259–3270. [11] E. Deeba, A. Korvin, E. L. Koh, A fuzzy difference equation with and Application, Journal of Difference Equations and applications, 2 (1996), 365–374. [12] P. Diamond, P. Kloeden, Metric Spaces of Fuzzy Sets, World Scientific, Singapore, 1994. [13] O. S. Fard, T. A. Bidgoli, Calculus of fuzzy functions on time scales (I), Soft Computing, 19 (2014), 293–305. [14] O. S. Fard, D. F. M. Torres, M. R. Zadeh, A Hukuhara approach to study of hybrid fuzzy systems on time scales, Applicable Analysis and Discrete Mathematics, 10 (2016), 152–167. [15] G. S. Guseinov, Integration on time scales, Journal of Mathematical Analysis and Applications, 285 (2003), 107– 127. [16] S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results in Mathematics, 18 (1990), 18–56. [17] S. Hong, Differentiability of multivalued functions on time scales and applications to multivalued dynamic equations, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), 3622–3637. [18] S. Hong, Y. Peng, Almost periodicity of set-valued functions and set dynamic equations on time scales, Information Sciences, 330 (2016), 157–174. [19] S. Hong, J. Gao, Y. Peng, Solvability and stability of impulsive set dynamic equations on time scales, Abstract Appl. Anal., vol. 2014, Article ID 610365, 19 pages, 2014. doi:10.1155/2014/610365. [20] A. Khastan, J.J. Nieto, R. Rodr´ıguez-L´opez, Variation of constant formula for first order fuzzy differential equations, Fuzzy Sets and Systems, 177 (2011), 20–33. [21] A. Khastan, R. Rodr´ıguez-L´opez, On the solutions to first order linear fuzzy differential equations, Fuzzy Sets and Systems, 295 (2016), 114–135. [22] A. Khastan, New solutions for first order linear fuzzy difference equations, Journal of Computational and Applied Mathematics, 312 (2017), 156–166. [23] V. Lakshmikantham, A. S. Vatsala, Basic Theory of Fuzzy Difference Equations, Journal of Fuzzy Difference Equations, 8 (2002), 957–968. [24] W. T. Li, H. R. Sun, Dynamics of rational difference equation, Applied Mathematics and Computation, 163 (2005), 577–591. [25] V. Lupulescu, Hukuhara differentiability of interval-valued functions and interval differential equations on time scales, Information Sciences, 248 (2013), 50–67. [26] M. Najariyan, M. Mazandarani, V.E. Balas, Solving first order linear fuzzy differential equations system, In: Balas V., Jain L., Balas M. (eds) Soft Computing Applications. SOFA 2016. Advances in Intelligent Systems and Computing, vol 634. Springer, Cham, 2018. [27] J. J. Nieto, R. Rodr´ıguez-L´opez, D. Franco, Linear first order fuzzy differential equations, International Journal of Uncertainty Fuzziness Knowledge-Based Syst, 14 (2006), 687–709. [28] C. Vasavi, G. S. Kumar, M. S. N. Murty, Generalized differentiability and integrability for fuzzy set-valued functions on time scales, Soft Computing, 20 (2016), 1093–1104. [29] C. Vasavi, G. S. Kumar, M. S. N. Murty, Fuzzy dynamic equations on time scales under second type Hukuhara delta derivative, International Journal of Chemical Science, 14 (2016), 49–66. [30] C. Vasai, G.S. Kumar, M. S. N. Murty, Fuzzy Hukuhara delta differential and applications to fuzzy dynamic equations on time scales, Journal of Uncertain Systems, 10 (2016), 163–180. [31] Q. Zhang, L. Yang, D. Liao, On the first fuzzy Riccati difference equation, Information Sciences, 270 (2014), 226–236. | ||
آمار تعداد مشاهده مقاله: 541 تعداد دریافت فایل اصل مقاله: 394 |