Abstract
In this paper, we give a new complex deformable derivative and integral of order λ which coincides with the classical derivative and integral for the special values of the parameters. We examine the basic properties of this derivative and integral. We also investigate the basic concepts of complex analysis for the λ-complex deformable derivative. Finally, we give some applications.
Keywords
Complex deformable derivative complex deformable integral complex deformable partial derivative λ-deformable Cauchy-Riemann equations λ-deformable analytic.
References
- Ahlfors, L. V., Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, Volume 177, Mcgraw-Hill, Newyork, 1953.
- Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264 (2014), 65–70. https://doi.org/10.1016/j.cam.2014.01.002
- Leibniz, G., Letter From Hanover, Germany to Johann g.f.a L’hospital, September 30, 1695, Leibniz Mathematische Schriften, Olms-Verlag, Hildeshein, Germany, 1965.
- Miller, K.S., An Introduction to the Fractional Calculus and Fractional Differential Equations, J. Wiley and Sons, New York, 1993.
- Oldham, K., Spanier, J., The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order, Elsevier, USA, 1974. https://doi.org/10.1016/s0076-5392(09)x6012-1
- Podlubny, I., Chechkin, A., Skovranek, T., Chen, Y., Jara, B. M. V., Matrix approach to discrete fractional calculus ii: partial fractional differential equations. Journal of Computational Physics, 228 (2009), 3137–3153. https://doi.org/10.1016/j.jcp.2009.01.014
- Zill, D., Shanahan, P., A First Course in Complex Analysis With Applications, Jones and Bartlett Learning, 2009.
- Zulfeqarr, F., Ujlayan, A., Ahuja, P., A new fractional derivative and its fractional integral with some applications. arXiv preprint arXiv:1705.00962 (2017), 1–11. https://doi.org/10.48550/arXiv.1705.00962
Abstract
References
- Ahlfors, L. V., Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, Volume 177, Mcgraw-Hill, Newyork, 1953.
- Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264 (2014), 65–70. https://doi.org/10.1016/j.cam.2014.01.002
- Leibniz, G., Letter From Hanover, Germany to Johann g.f.a L’hospital, September 30, 1695, Leibniz Mathematische Schriften, Olms-Verlag, Hildeshein, Germany, 1965.
- Miller, K.S., An Introduction to the Fractional Calculus and Fractional Differential Equations, J. Wiley and Sons, New York, 1993.
- Oldham, K., Spanier, J., The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order, Elsevier, USA, 1974. https://doi.org/10.1016/s0076-5392(09)x6012-1
- Podlubny, I., Chechkin, A., Skovranek, T., Chen, Y., Jara, B. M. V., Matrix approach to discrete fractional calculus ii: partial fractional differential equations. Journal of Computational Physics, 228 (2009), 3137–3153. https://doi.org/10.1016/j.jcp.2009.01.014
- Zill, D., Shanahan, P., A First Course in Complex Analysis With Applications, Jones and Bartlett Learning, 2009.
- Zulfeqarr, F., Ujlayan, A., Ahuja, P., A new fractional derivative and its fractional integral with some applications. arXiv preprint arXiv:1705.00962 (2017), 1–11. https://doi.org/10.48550/arXiv.1705.00962
Details
| Primary Language | English |
|---|---|
| Subjects | Real and Complex Functions (Incl. Several Variables) |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 21, 2024 |
| Submission Date | October 18, 2023 |
| Acceptance Date | March 18, 2024 |
| Published in Issue | Year 2024 Volume: 73 Issue: 2 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
