“…The properties of CmDLTr and CpDLTr have been discussed in [Ozzz] and [Adam4], respectively. For γ, δ ∈ (0, 1], let us now define the formula of the inverse fractional double Laplace transform [LDDL1;RdGw] for both conformable and Caputo fractional derivatives, denoted by ( xt γδ ) −1 [ Ψxt γδ (s 1 , s 1 )], as follows: Definition 9. Given an analytic function: Ψxt γδ (s 1 , s 2 ), for all s 1 , s 2 ∈ C and for γ, δ ∈ (0, 1] such that Re{s 1 ≥ η} and Re{s 2 ≥ σ}, where η, σ ∈ , then, the inverse fractional double Laplace transform (IFDLT) can be expressed [mkaabar] as follows:…”