Generalized derivative and π-derivative for set-valued functions

Information Sciences

Volumn 181, Issue 11, 2011, Pages 2177-2188

  Chalco Cano, Y ^a   Roman Flores H ^a   Jimenez Gamero M D ^b  

^a UNIVERSIDAD DE TARAPACÁ   (Chile)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Derivative for set valued functions; Differentiable set valued functions; Interval differential equations

Indexed keywords

DIFFERENTIABLE SET-VALUED FUNCTIONS; FUZZY FUNCTION; GENERALIZED DERIVATIVES; ILLUSTRATIVE EXAMPLES; INTERVAL DIFFERENTIAL EQUATIONS; INTERVAL-VALUED FUNCTION; SET-VALUED FUNCTIONS;

DIFFERENTIAL EQUATIONS;

EID: 79953282911     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2011.01.023     Document Type: Article

References (46)

1. T. Allahviranloo, N.A. Kiani, and M. Barkhordaria Toward the existence and uniqueness of solutions of second-order fuzzy differential equations Information Sciences 179 2009 1207 1215
2. T. Allahviranloo, N.A. Kiani, and N. Motamedib Solving fuzzy differential equations by differential transformation method Information Sciences 179 2009 955 956
3. J.P. Aubin, and A. Cellina Differential Inclusions 1984 Springer-Verlag New York
4. J.P. Aubin, and H. Franskowska Set-Valued Analysis 1990 Birkhäuser Boston
5. J.P. Aubin, and H. Franskowska Introduction: set-valued analysis in control theory Set-Valued Analysis 8 2000 1 9
6. S.M. Assev Quasilinear operators and their application in the theory of multivalued mappings Proceedings of the Steklov Institute of Mathematics 2 1986 23 52
7. R.P. Agarwal, and D. O'Regan Existence for set differential equations via multivalued operator equations Differential Equations and Applications vol. 5 2007 Nova Sci. Publ New York 1 5
8. H.T. Banks, and M.Q. Jacobs A differential calculus for multifunctions Journal of Mathematical Analysis and Applications 29 1970 246 272
9. B. Bede, and S.G. Gal Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equation Fuzzy Sets and Systems 151 2005 581 599 (Pubitemid 40305079)
10. B. Bede, I.J. Rudas, and A.L. Bencsik First order linear fuzzy differential equations under generalized differentiability Information Sciences 177 2007 1648 1662 (Pubitemid 46107427)
11. B. Bede Note on numerical solutions of fuzzy differential equations by predictor-corrector method Information Sciences 178 2008 1917 1922
12. F.S. De Blasi On the differentiability of multifunctions Pacific Journal of Mathematics 66 1976 67 81
13. F.S. De Blasi, V. Lakshmikantham, and T.G. Bhaskar An existence theorem for set differential inclusions in a semilinear metric space Control and Cybernetics 36 3 2007 571 582
14. Y. Chalco-Cano, H. Román-Flores, M.A. Rojas-Medar, Fuzzy differential equations with generalized derivative, in: Proceedings of 27th NAFIPS International Conference IEEE, 2008.
15. Y. Chalco-Cano, and H. Román-Flores On the new solution of fuzzy differential equations Chaos, Solitons & Fractals 38 2008 112 119 (Pubitemid 351503972)
16. Y. Chalco-Cano, and H. Román-Flores Comparison between some approaches to solve fuzzy differential equations Fuzzy Sets and Systems 160 2008 1517 -1527
17. Y. Chalco-Cano, M.A. Rojas-Medar, and H. Román-Flores Sobre ecuaciones diferenciales difusas Boletín de la Sociedad Española de Matemática Aplicada 41 2007 91 99
18. Y. Chalco-Cano, H. Román-Flores, M.D. Jiménez-Gamero, Fuzzy differential equation with π-derivative, in: Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009.
19. P. Diamond, and P. Kloeden Metric Space of Fuzzy Sets: Theory and Application 1994 World Scientific Singapore
20. P. Diamond Brief note on the variation of constants formula for fuzzy differential equations Fuzzy Sets and Systems 129 2002 65 71 (Pubitemid 34544383)
21. P. Diamond Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations IEEE Transactions on Fuzzy Systems 7 1999 734 740 (Pubitemid 32212164)
22. Z. Ding Ming Ma, and A. Kandel Existence of solutions of fuzzy differential equations with parameters Information Sciences 99 1997 205 217
23. T. Gnana Bhaskar, and V. Lakshmikantham Set differential equations and flow invariance Journal of Applied Analysis 82 2 2003 357 368 (Pubitemid 36571468)
24. M. Hukuhara Integration des applications mesurables dont la valeur est un compact convexe Funkcialaj Ekvacioj 10 1967 205 223
25. E. Hüllermeier An approach to modeling and simulation of uncertain dynamical systems International Journal Uncertainty, Fuzziness Knowledge-Bases Systems 5 1997 117 137 (Pubitemid 127532311)
26. A-G.M. Ibrahim On the differentiability of set-valued functions defined on a Banach space and mean value theorem Applied Mathematics and Computers 74 1996 76 94
27. L.J. Jowers, J.J. Buckley, and K.D. Reilly Simulating continuous fuzzy systems Information Sciences 177 2007 436 448 (Pubitemid 44634444)
28. V. Lakshmikantham, and A.A. Tolstonogov Existence and interrelation between set and fuzzy differential equations Nonlinear Analysis 55 3 2003 255 268
29. V. Lakshmikantham, and R. Mohapatra Theory of Fuzzy Differential Equations and Inclusions 2003 Taylor & Francis London
30. S. Markov Calculus for interval functions of a real variable Computing 22 1979 325 337
31. S. Mahmoud Taheri C-fuzzy numbers and a dual of extension principle Information Sciences 178 2008 827 835
32. R.E. Moore Interval Analysis 1966 Prince-Hall Englewood Cliffs, NJ
33. R.E. Moore Computational Functional Analysis 1985 Ellis Horwood Limited England
34. M. Misukoshi, Y. Chalco-Cano, H. Román-Flores, and R.C. Bassanezi Fuzzy differential equations and the extension principle Information Sciences 177 2007 3627 3635 (Pubitemid 46920529)
35. J.J. Nieto, and R. Rodríguez-López Euler polygonal method for metric dynamical systems Information Sciences 177 2007 4256 4270 (Pubitemid 47071913)
36. S. Pederson, and M. Sambandham Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem Information Sciences 179 2009 319 328
37. N.V. Plotnikova Systems of linear differential equations with π-derivative and linear differential inclusions Sbornik: Mathematics 196 2005 1677 1691 (Pubitemid 43449207)
38. M. Puri, and D. Ralescu Differential and fuzzy functions Journal of Mathematical Analysis and Applications 91 1983 552 558
39. H. Radströn An embedding theorem for spaces of convex sets Proceedings of the American Mathematical Society 3 1952 165 169
40. R. Rodriguez-López Comparison results for fuzzy differential equations Information Sciences 178 2008 1756 1779
41. L.J. Rodríguez-Muñis, M. López-Díaz, and M.A. Gil The s-differentiability of a fuzzy-valued mapping Information Sciences 151 2003 283 299
42. H. Román-Flores, and M. Rojas-Medar Embedding of level-continuous fuzzy sets on Banach spaces Information Sciences 144 2002 227 247 (Pubitemid 34763557)
43. L. Stefanini, and B. Bede Generalized Hukuhara differentiability of interval-valued functions and interval differential equations Nonlinear Analysis 71 2009 1311 1328
44. L. Stefanini A generalization of Hukuhara difference and division for interval and fuzzy arithmetic Fuzzy Sets and Systems 161 2010 1564 1584
45. S. Seikkala On the fuzzy initial value problem Fuzzy Sets and Systems 24 1987 319 -330
46. A. Tolstonogov Differential Inclusions in a Banach Space 2000 Kluwer Academic Publishers The Netherlands