Discrete version of fundamental theorems of fractional order integration for nabla operator
Authors
H. Byeon
- Department of AI-Big Data , Injevk University, Gimhae, 50833, Republic of Korea.
M. Abisha
- Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Tamil Nadu, India.
V. R. Sherine
- Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Tamil Nadu, India.
G. B. A. Xavier
- Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Tamil Nadu, India.
S. Prema
- Department of Mathematics, SRM Institute of science and Technology, Rampuram, Chennai 600089, Tamil Nadu, India.
V. Govindan
- Department of Mathematics,, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam 603103, Tamil Nadu, India.
H. Ahmad
- Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey.
- Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia.
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
- Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait.
D. Piriadarshani
- Department of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam 603103, Tamil Nadu, India.
S. El-Morsy
- Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia.
- Basic Science Department , Nile Higher Institute for Engineering and Technology, Mansoura, Egypt.
Abstract
The goal of this paper is to develop and present a precise theory for integer and fractional order \(\ell\)-nabla integration and its fundamental theorems. In our research work, we take two forms of higher order difference equation such as closed form and summation form. But most of the authors are focused only on the summation part only. Instead of finding the solution for the summation part, finding the solution for the closed gives the exact solution. To find the closed form solution for the integer order using the \(\ell\)-nabla operator, we used the factorial-coefficient method. For developing the theory of fractional order \(\ell\)-nabla operator and its integration, we introduce a function called \(N_{\nu}\)-type function. If the summation series is huge, this approach can help us to find the solution quickly. Suitable examples are provided for verification. Finally, we provide the application for detecting viral transmission using the nabla operator.
Share and Cite
ISRP Style
H. Byeon, M. Abisha, V. R. Sherine, G. B. A. Xavier, S. Prema, V. Govindan, H. Ahmad, D. Piriadarshani, S. El-Morsy, Discrete version of fundamental theorems of fractional order integration for nabla operator, Journal of Mathematics and Computer Science, 34 (2024), no. 4, 381--393
AMA Style
Byeon H., Abisha M., Sherine V. R., Xavier G. B. A., Prema S., Govindan V., Ahmad H., Piriadarshani D., El-Morsy S., Discrete version of fundamental theorems of fractional order integration for nabla operator. J Math Comput SCI-JM. (2024); 34(4):381--393
Chicago/Turabian Style
Byeon, H., Abisha, M., Sherine, V. R., Xavier, G. B. A., Prema, S., Govindan, V., Ahmad, H., Piriadarshani, D., El-Morsy, S.. "Discrete version of fundamental theorems of fractional order integration for nabla operator." Journal of Mathematics and Computer Science, 34, no. 4 (2024): 381--393
Keywords
- Mathematical operators
- problem solving
- nonlinear systems
- iterative methods
- discrete-nabla fractional calculus
- \(\mathcal{N}_{\nu}\)-type function
MSC
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