پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 628 |
| تعداد مقالات | 9,179 |
| تعداد مشاهده مقاله | 67,527,543 |
| تعداد دریافت فایل اصل مقاله | 8,062,165 |
Fuzzy q-Taylor Theorem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 13، دوره 16، شماره 8، آبان 2025، صفحه 161-178 اصل مقاله (4.14 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23034.2465 | ||
| نویسندگان | ||
| Zahra Noeiaghdam1؛ Morteza Rahmani2؛ Tofigh Allahviranloo* 3 | ||
| 1Department of Mathematics, Shahed University, Tehran, Iran | ||
| 2Faculty of Basic and Advanced Technologies in Biology, University of Science and Culture, Tehran, Iran | ||
| 3Quantum Technologies Research Center, (QTRC), Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran | ||
| تاریخ دریافت: 14 بهمن 1399، تاریخ پذیرش: 31 فروردین 1400 | ||
| چکیده | ||
| The main purpose of this work is to introduce and investigate fuzzy quantum calculus. Our idea begins with a general definition of fuzzy $q$-derivative on arbitrary time scales using the generalized Hukuhara difference. It compiled some basic facts in the fields of the fuzzy $q$-derivative and the fuzzy $q$-integral and proved them in detail. Proceed with this work, specifying the particular concept of fuzzy $q$-Taylor's expansion, especially for continuous and fuzzy valued functions which are non-differentiable in the classical (usual) concept, as the best tool for approximating functions and solving the fuzzy initial value $q$-problems. Eventually, some numerical examples of fuzzy $q$-Taylor's expansion of special functions and functions with switching points, are solved for illustration. | ||
| کلیدواژه‌ها | ||
| Generalized Hukuhara $q$-difference؛ $q$-Taylor's expansion؛ Fuzzy $q$-derivative؛ Fuzzy $q$-integral؛ Fuzzy $q$-Taylor | ||
| مراجع | ||
|
[1] T. Allahviranloo, Z. Noeiaghdam, and S. Noeiaghdam, J.J. Nieto, A fuzzy method for solving fuzzy fractional differential equations based on the generalized fuzzy Taylor expansion, Mathematics 8 (2020), no. 12, 2166. [2] T. Allahviranloo, Fuzzy Fractional Differential Operators and Equations, Springer, Cham, 2020. [3] T. Allahviranloo, Uncertain Information and Linear Systems, Springer, Cham, 2019. [4] T.V. Amit, K. Sheerin, and J.J. Gopal, A note on the convergence of fuzzy transformed finite difference methods, J. Appl. Math. Comput. 63 (2020), 143–170. [5] M.H. Annaby and Z.S. Mansour, q-Taylor and interpolation series for Jackson q-difference operators, J. Math. Anal. Appl. 344 (2008), 472–483. [6] A. Aral, V. Gupta, and R.P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, Science and Business Media, New York, 2013. [7] F.M. Atici and P.W. Eloe, Fractional q-calculus on a time scale, J. Nonlinear Math. Phys. 14 (2007), no. 3, 333–344. [8] T. Ernst, A new notation for q-Calculus a new q-Taylor’s formula, U.U.D.M. Report 1999:25, Department of Mathematics, Uppsala University, 1999. [9] H. Fakhri and S.E. Mousavi Gharalari, Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states, International J. Geom. Meth. Mod. Phys. 17 (2020), no. 2, 2050021. [10] H. Fakhri and M. Sayyah-Fard, Triplet q-cat states of the Biedenharn-Macfarlane q-oscillator with q > 1, Quantum Inf. Process. 19 (2020), 19. [11] H. Fakhri and V. Sayyah-Fard, q-coherent states associated with the noncommutative complex plane Cq2 for the Biedenharn-Macfarlane q-oscillator, Ann. Phys. 387 (2017), 14–28. [12] M.E.H. Ismail and D. Stanton, q-Taylor theorems, polynomial expansions, and interpolation of entire functions, J. Approx. Theory 123 (2003), 125–146. [13] F.H. Jackson, On q-functions and certain difference operator, Trans. Roy. Soc. Edin. 46 (1909), 253–281. [14] F.H. Jackson, On a q-definite integrals, Quart. J. Pure Appl. Math. 41 (1910), 193–203. [15] S.C. Jing and H.Y. Fan, q-Taylor’s formula with its q-remainder, Commun. Theore. Phys. 23 (1995), no. 1, 117–120. [16] V. Kac and P. Cheung, Quantum Calculus, Springer-Verlag, New York, Berlin, Heidelberg, 2001. [17] R. Koekoek, P.A. Lesky, and R.F. Swarttouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, Springer Monographs in Mathematics, Springer-Verlag, Berlin, Heidelberg, 2010. [18] B. Lopez, J.M. Marco, and J. Parcet, Taylor series for the Askey-Wilson operator and classical summation formulas, Proc. Amer. Math. Soc. 134 (2006), no. 8, 2259–2270. [19] J.M. Marco and J. Parcet, A new approach to the theory of classical hypergeometric polynomials, Trans. Amer. Math. Soc. 358 (2006), no. 1, 183–214. [20] N. Mikaeilvand, Z. Noeiaghdam, S. Noeiaghdam, and J.J. Nieto, A novel technique to solve the fuzzy system of equations, Mathematics 8 (2020), no. 5, 850. [21] Z. Noeiaghdam, T. Allahviranloo, and J.J. Nieto, q-Fractional differential equations with uncertainty, Soft Com[1]put. 23 (2019), 9507–9524. [22] Z. Noeiaghdam, M. Rahmani, and T. Allahviranloo, Introduction of the numerical methods in quantum calculus with uncertainty, J. Math. Model. 9 (2021), no. 2, 303–322. [23] Z.M. Odibat and N.T. Shawagfeh, Generalized Taylor’s formula, Appl. Math. Comput. 186 (2007), 286–293. [24] M. Xin-You and W.U. Yu-Qian, Dynamical analysis of a fuzzy phytoplankton-zooplankton model with refuge, fishery protection and hervesting, J. Appl. Math. Comput. 63 (2020), 361–389. | ||
|
آمار تعداد مشاهده مقاله: 57 تعداد دریافت فایل اصل مقاله: 94 |
||