اخبار و اعلانات
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 550 |
| تعداد مقالات | 5,705 |
| تعداد مشاهده مقاله | 7,969,889 |
| تعداد دریافت فایل اصل مقاله | 5,351,914 |
System of fuzzy fractional differential equations in generalized metric space | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 10، دوره 16، شماره 2، خرداد و تیر 2019، صفحه 107-121 اصل مقاله (236.45 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2019.4546 | ||
| نویسندگان | ||
Long Viet Hoang  1؛ Nguyen Thi Kim Son 2؛ Phuong Hoang Thao3
| ||
| 1Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam. | ||
| 2Center for Science and Technology Information, Hanoi Metropolitan University, 98 Duong Quang Ham, Quan Hoa, Cau Giay, Ha Noi, Viet Nam | ||
| 3Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam | ||
| چکیده | ||
| In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of complete generalized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergent matrix technique with Schauder fixed point principle of vector valued operators in semilinear Banach spaces. Some computational examples are represented to demonstrate our theoretical results. | ||
| کلیدواژه‌ها | ||
| Fuzzy fractional differential systems؛ Caputo gH-derivatives؛ vector valued metric؛ generalized metric space | ||
| مراجع | ||
|
[1] R. P. Agarwal, V. Lakshmikantham, J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Analysis, 72 (2010), 2859-2862. [2] R. P. Agarwal, S. Arshad, D. O’Regan, V. Lupulescu, Fuzzy fractional integral equations under compactness type condition, Fractional Calculus and Applied Analysis, 15 (2012), 572-590. [3] R. P. Agarwal, S. Arshad, D. O’Regan, V. Lupulescu, A Schauder fixed point theorem in semilinear spaces and applications, Fixed Point Theory and Applications, 2013, (2013):306, 1-13. [4] A. Ahmadian, S. Salahshour, D. Baleanu, H. Amirkhani, R. Yunus,Tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the Oil Palm Frond as a promising source of xylose, Journal of Computational Physics, 294 (2015), 562-584. [5] A. Ahmadian, S. Salahshour, C. S. Chan, Fractional differential systems: a fuzzy solution based on operational matrix of shifted Chebyshev polynomials and its applications, IEEE Xplore: IEEE Transactions on Fuzzy Systems, 25 (2016), 218-236. [6] A. Ahmadian, S. Salahshour, C. S. Chan, D. Baleanu, Numerical solutions of fuzzy differential equations by an efficient Runge-Kutta method with generalized differentiability, Fuzzy Sets and Systems, 331 (2018), 47-67. [7] T. Allahviranloo, S. Salahshour, S. Abbasbandy, Explicit solutions of fractional differential equations with uncertainty, Soft Computing, 16 (2012), 297-302. [8] T. Allahviranloo, Z. Gouyandeh, A. Armand, Fuzzy fractional differential equations under generalized fuzzy Caputo derivative, Journal of Intelligent & Fuzzy Systems, 26 (2014), 1481-1490. [9] B. Bede, Mathematics of Fuzzy Sets and Fuzzy Logic, Springer-Verlag Berlin Heidelberg, 2013. [10] B. Bede, L. Stefanini, Generalized differentiability of fuzzy valued functions, Fuzzy Sets and Systems, 230 (2013), 119-141. [11] A. Boucherif, R. Precup, On the nonlocal initial value problem for first order differential equations, Fixed Point Theory, 4 (2003), 121-133. [12] L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Journal of Applied Analysis , 40 (1991), 11-19. [13] L. Byszewski, Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, Journal of Mathematical Analysis and Applications, 162 (1991), 494-505. [14] N. V. Hoa, Fuzzy fractional functional differential equations under Caputo gH-differentiability, Communications in Nonlinear Science and Numerical Simulation, 22 (2015), 1134-1157. [15] N. V. Hoa, Fuzzy fractional functional integral and differential equations, Fuzzy Sets and Systems, 280 (2015), 58-90. [16] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol 204. North-Holland Mathematics Studies. Elsevier, Amsterdam, 2006. [17] H. V. Long, N. T. K. Son, N. T. M. Ha, L. H. Son, The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations, Fuzzy Optimization and Decision Making, 13 (2014), 435-462. [18] H. V. Long, N. T. K. Son, H. T. T. Tam, Global existence of solutions to fuzzy partial hyperbolic functional differential equations with generalized Hukuhara derivatives, Journal of Intelligent & Fuzzy Systems, 29 (2015), 939-954. [19] H. V. Long, N. K. Son, H. T. Tam, J. C. Yao, Ulam Stability for fractional partial integro-differential equation with uncertainty, Acta Mathematica Vietnamica, 42 (2017), 675-700. [20] H. V. Long, N. T. K. Son, N. V. Hoa, Fuzzy fractional partial differential equations in partially ordered metric spaces, Iranian Journal of Fuzzy Systems, 14(2) (2017), 107-126. [21] H. V. Long, N. K. Son, H. T. Tam, The solvability of fuzzy fractional partial differential equations under Caputo gH-differentiability, Fuzzy Sets and Systems, 309 (2017), 35-63. [22] H. V. Long, J. J. Nieto, N. T. K. Son, New approach to study nonlocal problems for differential systems and partial differential equations in generalized fuzzy metric spaces, Fuzzy Sets and Systems, 331 (2018), 26-46. [23] M. T. Malinowski, On random fuzzy differential equations, Fuzzy Sets and Systems, 160 (2009), 3152-3165. [24] M. T. Malinowski, Random fuzzy differential equations under generalized Lipschitz condition, Nonlinear Analysis (RWA), 13(2) (2012), 860-881. [25] M. T. Malinowski, Random fuzzy fractional integral equations-theoretical foundations, Fuzzy Sets and Systems, 265 (2015), 39-62. [26] M. Mazandarani, A. Vahidian Kamyad, Modified fractional Euler method for solving fuzzy fractional initial value problem, Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 12-21. [27] N. Octavia, R. Precup, On the nonlocal initial value problem for first order differential systems, Studia Universitatis Babes-Bolyai Mathematica, 56 (2001), 113-125. [28] N. Octavia, R. Precup, Implicit first order differential systems with nonlocal conditions, Electronic Journal of Qualitative Theory of Differential Equations, 69 (2014), 1-13. [29] R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002. [30] H. Rom´aan-Flores, M. Rojas-Medar, Embedding of level-continuous fuzzy sets on Banach spaces, Information Sciences, 144 (2002), 227-247. [31] S. Salahshour, T. Allahviranloo, S. Abbasbandy, D. Baleanu, Existence and uniqueness results for fractional differential equations with uncertainty, Advances in Difference Equations, 112 (2012), 1-12. [32] S. Salahshour, A. Ahmadian, N. Senu, D. Baleanu, P. Agarwal, On analytical solutions of the fractional differential equation with uncertainty: application to the Basset Problem, Entropy, 17 (2015), 885-902. [33] S. Salahshour, A. Ahmadian, F. Ismail, D. Baleanu, A novel integral fuzzy solution for fuzzy linear system, Entropy, 18 (2016), 68. [34] S. Salahshour, A. Ahmadian, F. Ismail, D. Baleanu, A fractional derivative with non-singular kernel for interval valued functions under uncertainty, Optik - International Journal for Light and Electron Optics, 130 (2017), 273-286. [35] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, 1993. [36] M. P. Sapagovas, The difference method for the solution of the problem on the equilibrium of a drop of liquid, Differ. Uravn. Primen., 31 (1978), 63-72. (in Russian) [37] L. Stefanini, B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis, 71 (2009), 1311-1328. | ||
|
آمار تعداد مشاهده مقاله: 870 تعداد دریافت فایل اصل مقاله: 344 |
||
