جواب عددی از معادلات دیفرانسیل فازی هیبریدی مرتبه دوم با دیفرانسیل پذیری تعمیم یافته
Subject Areas : International Journal of Industrial Mathematicsنیره شهریاری 1 , سعید عباسبندی 2
1 - گروه ریاضی، واحد علوم و تحقیقات تهران، دانشگاه آزاد اسلامی، تهران، ایران.
2 - گروه ریاضی، دانشکده علوم پایه، دانشگاه بین المللی امام خمینی(ره)، قزوین، ایران.
Keywords: معادلات دیفرانسیل فازی هیبریدی, معادلات دیفرانسیل فازی, بسط تیلور فازی, دیفرانسیل پذیری هاکوهارای تعمیم یافته, gH- دیفرانسیل پذیر,
Abstract :
در این مقاله، یک روش عددی برای حل معادلات دیفرانسیل فازی هیبریدی مرتبه دوم با استفاده از بسط تیلور فازی تحت دیفرانسیل پذیری تعمیم یافته هاکوهارا و همچنین قضیه همگرایی ارائه شده است. همچنین کاربرد روش با حل چندین مثال عددی نشان داده شده است. نتایج نهایی نشان دهنده جواب معادلات دیفرانسیل فازی هیبریدی مرتبه دوم است.
[1] S. Abbasbandy, T. Allahviranloo, O. LopezPouso, J. J. Nieto, Numerical methods for fuzzy differential inclusions, Journal of Computer and Mathematics with Applications 48 (2004) 1633-1641.
[2] T. Allahviranloo, A. Armand, Z. Gouyandeh, Fuzzy fractional differential equations under generalized fuzzy Caputo derivative, Journal of Intelligent and Fuzzy Systems 26 (2014) 1481-1490.
[3] T. Allahviranloo, Z. Gouyandeh, A. Armand, A full fuzzy method for solving differential equation based on Taylor expansion, Journal of Intelligent and Fuzzy Systems 29 (2015) 1039-1055.
[4] T. Allahviranloo, N. A. Kiani, M. Barkhordari, Toward the existence and uniqueness of second-order differential equations, Information sciences 179 (2009) 1207-1215.
[5] G. A. Anastassiou, Fuzzy mathematics: Approximation theory, Studies in Fuzziness and Soft Computing 251 (2010) 267-271.
[6] R. J. Aumann, Integrals of set-valued functions, Journal of Computer and Mathematics with Applications 12 (1965) 1-12.
[7] B. Bede, S. G. Gal, Almost Periodic fuzzynumber valued functions, Fuzzy sets and systems 147 (2004) 385-403.
[8] B. Bede, S. G. Gal, Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations, Fuzzy sets and systems 151 (2005) 581-599.
[9] B. Bede, I. J. Rudas, L. Attila, First order linear fuzzy differential equations under generalized differentiability, Information sciences 177 (2007) 3627-3635.
[10] B. Bede, L. Stefanini, Generalized differentiability of fuzzy valued functions, Fuzzy Sets and Systems 230 (2013) 119-141.
[11] J. Buckley, T. Feuring, Fuzzy differential equations, Fuzzy sets and systems 110 (2000) 43-54.
[12] Y. Chalco-Cano, H. Roman-Flores, On new solutions of fuzzy differential equations, Chaos, Solitons and Fractals (2006) 1016-1043.
[13] W. Congxin, M. Ming, Embedding problem of fuzzy number space: part III, Fuzzy sets and systems 46 (1992) 281-286.
[14] R. Goestschel, W. Voxman, Elementary fuzzy calculus, Fuzzy sets and systems 43 (1991) 159-171.
[15] Z. Guang{Quan, Fuzzy continuous function and its properties, Fuzzy sets and systems 24 (1987) 31-43.
[16] O. Kaleve, Fuzzy differential equations, Fuzzy sets and systems 24 (1987) 301-317.
[17] A. Khastan, F. Bahrami, K. Ivaz, New results on multiple solutions for N-order fuzzy differential under Generalized Differentiability, Boundary Value Problem 20 (2009) 395-414.
[18] M. Ma, M. Friedman, A. Kandel, Numerical solutions of fuzzy differential equations, Fuzzy sets and systems 105 (1999) 133-138.
[19] J. J. Nieto, A. Khastan, K. Ivaz, Numerical solution of fuzzy differential equations under generalized differentiability, Nonlinear Anal. Hybrid System 3 (2009) 700-707.
[20] P. Parkash, V. Kalaiselvi, Numerical solution of hybrid fuzzy differential equations by predictor-corrector method, International Journal of Computer Mathematics 86 (2009) 121-134.
[21] S. Pederson, M. Sambandham, Numerical solution to hybrid fuzzy systems, Mathematical and Computer Modelling 45 (2007) 1133-1144.
[22] S. Pederson, M. Sambandham, Numerical solution of hybrid fuzzy differential equation IVP by characterization theorem, Information sciences 179 (2009) 319-328.
[23] L. Stefanini, B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis 71 (2009) 1311-1328.
[24] H.C. Wu, The improper fuzzy Riemann integral and its numerical integration,Information sciences 111 (1999) 109-137.
464 N. Shahryari et al., /IJIM Vol. 13, No. 4 (2021) 451-464
[25] H.C. Wu, The fuzzy Riemann integral and
its numerical integration, Fuzzy sets and systems 110 (2000) 1-25.