On triple g transformation and its properties

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 〗