On triple g transformation and its properties

Authors

DOI:

https://doi.org/10.31185/wjcms.177

Keywords:

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

2023-09-30

Issue

Section

Mathematics

How to Cite

[1]
Ahmed Mahdi Abbood, “On triple g transformation and its properties ”, WJCMS, vol. 2, no. 3, pp. 23–29, Sep. 2023, doi: 10.31185/wjcms.177.