**R. U. Ndubuisi, U. K. Nwajeri, C. P. Onyenegecha, K. M. Patil, O. G. Udoaka and W. I. Osuji**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 28, 2022, Number 4, Pages 698–709

DOI: 10.7546/nntdm.2022.28.4.698-709

**Full paper (PDF, 549 Kb)**

## Details

### Authors and affiliations

R. U. Ndubuisi

*Department of Mathematics, Federal University of Technology
Owerri, Nigeria*

U. K. Nwajeri

*Department of Mathematics, Federal University of Technology
Owerri, Nigeria*

C. P. Onyenegecha

*Department of Physics, Federal University of Technology
Owerri, Nigeria*

K. M. Patil

*Department of Mathematics, Dharmsinh Desai University
India*

O. G. Udoaka

*Department of Mathematics, Akwa Ibom State University
Ikot Akpaden, Nigeria*

W. I. Osuji

*Department of Mathematics, Federal University of Technology
Owerri, Nigeria*

### Abstract

This paper considers linear mappings in paraletrix spaces as an extension of the one given for rhotrix vector spaces. Furthermore, the adjoints of these mappings are given with their application in fractional calculus.

### Keywords

- Heart-oriented paraletrix
- Linear mapping
- Adjoints
- Inner product
- Fractional calculus
- Rhotrix

### 2020 Mathematics Subject Classification

- 20M10

### References

- Ajibade, A. O. (2003).The concept of Rhotrix in mathematical enrichment.
*International Journal of Mathematical Education in Science and Technology*, 34, 175–179. - Aminu, A. (2010). Rhotrix vector spaces.
*International Journal of Mathematical*

*Education in Science and Technology*, 41(4), 531–538. - Aminu, A. (2010). An example of linear mappings: extension to rhotrices.
*International Journal of Mathematical Education in Science and Technology*, 41(5), 691–698. - Aminu, A., & Michael, O. (2014). An introduction to the concept of paraletrix, a

generalization of rhotrix.*Afrika Matematica*, 26, 871–885. - Atanassov, K. T., & Shannon, A. G. (1998). Matrix-Tertions and Matrix-Noitrets: Exercise for Mathematical Enrichment.
*International Journal of Mathematical Education in Science and Technology*, 29, 898–903. - Carpinteri, A. & Mainardi, F. (1977).
*Fractals and Fractional Calculus in Continuum Mechanisms*. Springer-Verlag Wien GmbH, No. 378. - Fernandez, A., Ozarslan, M. A., & Baleanu, D. (2019). On fractional calculus with

general analytic kernels.*Applied Mathematics and Computation*, 354, 248–265. - Kreyszig, E. (1978).
*Introductory Functional Analysis with Applications*. Wiley & Sons. Inc. - Ndubuisi, R. U., Abubakar, R. B., Udoaka, O. G., & Ugbene, I. J. (2021). Characterization of a heart-oriented paraletrix.
*Journal of Mathematical and Computational Science*, 11(3), 3130–3150. - Nwajeri, U. K, Omame, A., & Onyenegecha, C. P. (2021). Analysis of a fractional order model for HPV and CT co-infection.
*Results in Physics*, 28,104643. - Oldham, K. B., & Spanier, J. (1974).
*The Fractional Calculus*. Academic Press, New York. - Oni, M., & Aminu, A. (2015). Paraletrix linear space.
*Journal of the Nigerian Association of Mathematical Physics*, 31, 279–284. - Omame, A., Nwajeri, U. K, Abbas, M., & Onyenegecha, C. P. (2022). A fractional order control model for diabetes and Covid-19 co-dynamics with Mittag-Leffler.
*Alexandria Engineering Journal*, 61(10), 7619–7635. - Omame, A., Okuonghae, D., Nwajeri, U. K., & Onyenegecha, C. P. (2021). A fractional order multi-vaccination model for Covid-19 with non-singular kernel.
*Alexandria**Engineering Journal*, 61(8), 6089–6104. - Podlubny, I. (1999).
*Fractional Differential Equations*. Academic Press, San Diego, Vol. 198. - Sani, B. (2004). An alternative method for multiplication of rhotrices.
*International**Journal of Mathematical Education in Science and Technology*, 35, 777–781. - Stephen, B., & Lieven, V. (2018).
*Introduction to Applied Linear Algebra: Vectors,**Matrices and Least-Squares*. Cambridge University Press.

### Manuscript history

- Received: 3 June 2022
- Revised: 25 October 2022
- Accepted: 27 October 2022
- Online First: 31 October 2022

## Related papers

- Atanassov, K. T. (2023). On tertions and other algebraic objects.
*Notes on Number Theory and Discrete Mathematics*, 29(4), 861-880.

## Cite this paper

Ndubuisi, R. U., Nwajeri, U. K., Onyenegecha, C. P., Patil, K. M., Udoaka, O. G., & Osuji, W. I. (2022). Linear mappings in paraletrix spaces and their application to fractional calculus. *Notes on Number Theory and Discrete Mathematics*, 28(4), 698-709, DOI: 10.7546/nntdm.2022.28.4.698-709.