\(\overline{\varphi({\tt{x}})}\)-Tribonnaci polynomial, numbers, and its sum
Authors
R. Pandurangan
- Department of Mathematics, School of Engineering and Technology, Dhanalakshmi Srinivasan University, Samayapuram, Tiruchirapalli District, Tamil Nadu-621 112, India.
S. Kannan
- Department of Mathematics, St. Joseph’s College of Engineering, Old Mahabalipuram Road, Chennai,Tamilnadu-600 119, India.
S. T. M. Thabet
- Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India.
- Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen.
- Department of Mathematics, College of Science, Korea University, Seoul 02814, South Korea.
M. Vivas-Cortez
- Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Quito, Ecuador.
I. Kedim
- Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia.
Abstract
This study presents a general third-order nabla difference operator that allows us to get \(\overline{\varphi({\tt{x}})}\)-Tribonacci sequences,
Tribonacci numbers, and their sum using the coefficients of different trigonometric functions and their
inverse. In this section, we examined the numerical solutions and \(C^*\)-solutions of the
\(\overline{\varphi({\tt{x}})}\)-Tribonacci sequences for different functions. In addition,
some interesting conclusions and theorems are obtained for the sum of the terms of the Tribonacci
sequence. Also, we offer appropriate examples to show how to use MATLAB to demonstrate our results.
Share and Cite
ISRP Style
R. Pandurangan, S. Kannan, S. T. M. Thabet, M. Vivas-Cortez, I. Kedim, \(\overline{\varphi({\tt{x}})}\)-Tribonnaci polynomial, numbers, and its sum, Journal of Mathematics and Computer Science, 37 (2025), no. 1, 32--44
AMA Style
Pandurangan R., Kannan S., Thabet S. T. M., Vivas-Cortez M., Kedim I., \(\overline{\varphi({\tt{x}})}\)-Tribonnaci polynomial, numbers, and its sum. J Math Comput SCI-JM. (2025); 37(1):32--44
Chicago/Turabian Style
Pandurangan, R., Kannan, S., Thabet, S. T. M., Vivas-Cortez, M., Kedim, I.. "\(\overline{\varphi({\tt{x}})}\)-Tribonnaci polynomial, numbers, and its sum." Journal of Mathematics and Computer Science, 37, no. 1 (2025): 32--44
Keywords
- Generalized nabla difference operator with trigonometric coefficients
- generalized Tribonacci sequence
- \(N^*\)-solution
- \(C^*\)-solution
- Tribonacci summation
MSC
- 39A70
- 39A10
- 47B39
- 65J10
- 65Q10
References
-
[1]
M. S. Abdo, T. Abdeljawad, S. M. Ali, K. Shah, F. Jarad, Existence of positive solutions for weighted fractional order differential equations, Chaos Solitons Fractals, 141 (2020), 8 pages
-
[2]
D. Brightlin, D. Babu, Heat equation obtained by q-difference operator with two variable, J. Comput. Math., 6 (2022), 46–52
-
[3]
T. Cai, Perfect numbers and Fibonacci sequences, World Scientific Publishing Co., Hackensack (2022)
-
[4]
A. D. Chavan, C. V. Suryawanshi, Correlation of Fibonacci sequence and golden ratio with its applications in engineering and science, Int. J. Eng. Manag. Res. (IJEMR), 10 (2020), 31–36
-
[5]
M. M. Dzherbashian, A. B. Nersesian, Fractional derivatives and Cauchy problem for differential equations of fractional order, Fract. Calc. Appl. Anal., 23 (2020), 1810–1836
-
[6]
R. Hilfer, Applications of fractional calculus in physics, World Scientific Publishing Co., River Edge (2000)
-
[7]
T. Jin, H. Xia, Lookback option pricing models based on the uncertain fractional-order differential equation with Caputo type, J. Ambient Intell. Humaniz. Comput., 14 (2023), 6435–6448
-
[8]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B.V., Amsterdam (2006)
-
[9]
T. Koshy, Fibonacci and Lucas numbers with applications. Vol. 2, John Wiley & Sons, Hoboken (2019)
-
[10]
K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley & Sons, New York (1993)
-
[11]
A. K. Pandey, S. Kanchan, A. K. Verma, Applications of Fibonacci Sequences and Golden Ratio, J. Inform. Electr. Electron. Eng. (JIEEE), 4 (2023), 1–11
-
[12]
K. Shah, M. Arfan, A. Ullah, Q. Al-Mdallal, K. J. Ansari, T. Abdeljawad, Computational study on the dynamics of fractional order differential equations with applications, Chaos Solitons Fractals, 157 (2022), 17 pages
-
[13]
N. A. Shah, Y. S. Hamed, K. M. Abualnaja, J.-D. Chung, R. Shah, A. Khan, A comparative analysis of fractional-order Kaup-Kupershmidt equation within different operators, Symmetry, 14 (2022), 23 pages
-
[14]
S. Sinha, The Fibonacci numbers and its amazing applications, Int. J. Eng. Sci. Invent., 6 (2017), 7–14
-
[15]
S. T. M. Thabet, M. B. Dhakne, On boundary value problems of higher order abstract fractional integro-differential equations, Int. J. Nonlinear Anal. Appl., 7 (2016), 165–184
-
[16]
S. T. M. Thabet, M. B. Dhakne, On positive solutions of higher order nonlinear fractional integro-differential equations with boundary conditions, Malaya J. Mat., 7 (2019), 20–26
-
[17]
S. T. M. Thabet, M. B. Dhakne, M. A. Salman, R. Gubran, Generalized fractional Sturm-Liouville and Langevin equations involving Caputo derivative with nonlocal conditions, Progr. Fract. Differ. Appl., 6 (2020), 225–237
-
[18]
S. T. M. Thabet, M. M. Matar, M. A. Salman, M. E. Samei, M. Vivas-Cortez, I. Kedim, On coupled snap system with integral boundary conditions in the G-Caputo sense, AIMS Math., 8 (2023), 12576–12605
-
[19]
G. B. A. Xavier, P. Rajiniganth, M. M. S. Manuel, V. Chandrasekar, Forward ( , )-difference operator nd its some applications in number theory, Int. J. Appl. Math., 25 (2012), 109–124
-
[20]
T. K. Yuldashev, B. J. Kadirkulovich, Nonlocal problem for a mixed type fourth-order differential equation with {H}ilfer fractional operator, Ural Math. J., 6 (2020), 153–167
