# zbMATH — the first resource for mathematics

On new solutions of fuzzy differential equations. (English) Zbl 1142.34309
Summary: We study fuzzy differential equations (FDE) using the concept of generalized H-differentiability. This concept is based in the enlargement of the class of differentiable fuzzy mappings and, for this, we consider the lateral Hukuhara derivatives. We will see that both derivatives are different and they lead us to different solutions from a FDE. Also, some illustrative examples are given and some comparisons with other methods for solving FDE are made.

##### MSC:
 34A60 Ordinary differential inclusions 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text:
##### References:
 [1] Abbod, M.F.; Von Keyserlingk, D.G.; Linkens, D.A.; Mahfouf, M., Survey of utilisation of fuzzy technology in medicine and healthcare, Fuzzy set syst, 120, 331-349, (2001) [2] Abbasbandy, S.; Nieto, J.J.; Alavi, M., Tuning of reachable set in one dimensional fuzzy differential inclusions, Chaos, solitons & fractals, 26, 1337-1341, (2005) · Zbl 1073.65054 [3] Barro, S.; Marı´n, R., Fuzzy logic in medicine, (2002), Physica-Verlag Heidelberg [4] Bede, B.; Gal, S.G., Almost periodic fuzzy-number-valued functions, Fuzzy set syst, 147, 385-403, (2004) · Zbl 1053.42015 [5] Bede, B.; Gal, S.G., Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations, Fuzzy set syst, 151, 581-599, (2005) · Zbl 1061.26024 [6] Bencsik A, Bede B, Tar J, Fodor J, Fuzzy differential equations in modeling hydraulic differential servo cylinders, In: Third Romanian-Hungarian joint symposium on applied computational intelligence (SACI), Timisoara, Romania, 2006. [7] Congxin, W.; Shiji, S., Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditions, Inform sci, 108, 123-134, (1998) · Zbl 0931.34041 [8] Datta, D.P., The Golden Mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology, Chaos, solitons& fractals, 17, 781-788, (2003) · Zbl 1032.26502 [9] Diamond, P., Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations, IEEE trans fuzzy syst, 7, 734-740, (1999) [10] Diamond, P., Brief note on the variation of constants formula for fuzzy differential equations, Fuzzy set syst, 129, 65-71, (2002) · Zbl 1021.34048 [11] El Naschie, M.S., On a fuzzy Kähler manifold which is consistent with the two slit experiment, Int J nonlinear sci numer simul, 6, 95-98, (2005) [12] El Naschie, M.S., From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold, Chaos, solitons & fractals, 25, 969-977, (2005) · Zbl 1070.81118 [13] Feng, G.; Chen, G., Adaptative control of discrete-time chaotic systems: a fuzzy control approach, Chaos, solitons & fractals, 253, 459-467, (2005) · Zbl 1061.93501 [14] Gnana Bhaskar, T.; Lakshmikantham, V.; Devi, V., Revisiting fuzzy differential equations, Nonlinear anal, 58, 351-358, (2004) · Zbl 1095.34511 [15] Guo, M.; Xue, X.; Li, R., The oscillation of delay differential inclusions and fuzzy biodynamics models, Math comput model, 37, 651-658, (2003) · Zbl 1057.34076 [16] Guo, M.; Li, R., Impulsive functional differential inclusions and fuzzy population models, Fuzzy set syst, 138, 601-615, (2003) · Zbl 1084.34072 [17] Hanss, M., Applied fuzzy arithmetic: an introduction with engineering applications, (2005), Springer-Verlag Berlin · Zbl 1085.03041 [18] Hullermeier, E., An approach to modeling and simulation of uncertain dynamical systems, Int J uncertainty, fuzziness knowledge-bases syst, 5, 117-137, (1997) · Zbl 1232.68131 [19] Kaleva, O., Fuzzy differential equations, Fuzzy set syst, 24, 301-317, (1987) · Zbl 0646.34019 [20] Kaleva, O., A note on fuzzy differential equations, Nonlinear anal, 64, 895-900, (2006) · Zbl 1100.34500 [21] Negoita CV, Ralescu DA, Applications of fuzzy sets to system analysis, Birkhauser, Basel, 1975. [22] Nieto, J.J.; Rodrı´guez-López, R., Bounded solutions for fuzzy differential and integral equations, Chaos, solitons & fractals, 27, 1376-1386, (2006) · Zbl 1330.34039 [23] Oberguggenberger, M.; Pittschmann, S., Differential equations with fuzzy parameters, Math mod syst, 5, 181-202, (1999) · Zbl 0961.34047 [24] Puri, M.; Ralescu, D., Differential and fuzzy functions, J math anal appl, 91, 552-558, (1983) · Zbl 0528.54009 [25] Román-Flores, H.; Rojas-Medar, M., Embedding of level-continuous fuzzy sets on Banach spaces, Inform sci, 144, 227-247, (2002) · Zbl 1034.46079 [26] Román-Flores, H.; Chalco-Cano, Y., Robinson’s chaos in set-valued discrete systems, Chaos, solitons & fractals, 25, 33-42, (2005) · Zbl 1071.37013 [27] Román-Flores, H.; Chalco-Cano, Y., Some chaotic properties of zadeh’s extension, Chaos, solitons & fractals, 35, 452-459, (2008) · Zbl 1142.37308 [28] Vorobiev, D.; Seikkala, S., Toward the theory of fuzzy differential equations, Fuzzy set syst, 125, 231-237, (2002) · Zbl 1003.34046 [29] Zhang, H.; Liao, X.; Yu, J., Fuzzy modeling and synchronization of hyperchaotic sytems, Chaos, solitons & fractals, 26, 835-843, (2005) · Zbl 1093.93540
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.