On triple g transformation and its properties
DOI:
https://doi.org/10.31185/wjcms.177Keywords:
Triple transformation, Mittag-Leffler function, T-transformation, Fractional convolution problem, Integral transform.Abstract
In this paper, we defined new triple transformation, which is called the fractional triple g-transformation of the order αl ,0<α≤1 for fractional of differentiable functions. This transformation is generalized to double g-transformation. Which has the following form;
Tg_α (u(ξ,τ,μ)=p(s)∫_0^∞▒∫_0^∞▒∫_0^∞▒〖E_α 〖(-(q_1 (s)ξ+q_2 (s)τ+q_3 (s)μ)〗^α 〖(dξ)〗^α 〖(dτ)〗^α 〖(dμ)〗^α 〗
References
H. Jafari, “A new general integral transform for solving integral equations,” J. Adv. Res, vol. 32, pp. 133–138, 2021.
A. Apelblat, “Differentiation of the mittag-leffier functions with respect to parameters in the laplace transform approach,” Mathematics, vol. 8, no. 5, 2020.
H. J. Haubold, “Mittag-Leffler Functions and Their Applications,” J. Appl. Math, vol. 1, pp. 1–51, 2011.
R. J. Al-Owaidi and M. H. Geem, “Solving Fractional Partial Differential Equations by Triple g-Transformation,” J. Al-Qadisiyah for Comput. Sci. Math, vol. 15, no. 1, pp. 86–91, 2023.
A. Abbood and A. M. H. Geem, “Double α-g-Transformation and Its Properties,” J. Al-Qadisiyah for Comput. Sci. Math, vol. 14, no. 3, pp. 33–41, 2022.
M. Meddahi, H. Jafari, and X. J. Yang, “Towards new general double integral transform and its applications to differential equations,” Math. Methods Appl. Sci, vol. 45, no. 4, pp. 1916–1933, 2022.
R, J. Hadi, and A. M. H. Geem, “On Triple g-Transformation and Its Properties,” J. Al-Qadisiyah for Comput. Sci. Math, vol. 14, no. 4, pp. 174–183.
M. A. Khan and S. Ahmed, “On some properties of the generalized Mittag-Leffler function,” SpringerPlus, vol. 2, pp. 337–337, 2013.
G. D. Medina, “Fractional Laplace Transform and Fractional Calculus,” J. Int. Math. Forum, pp. 991–999, 2017
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Ahmed Mahdi Abbood
This work is licensed under a Creative Commons Attribution 4.0 International License.