Table 4: Jeffrey viscoelastic medium.

              Model Constitutive equation
        ξ‚΅ 1 πœ€ = πœ‚ 1 πœ• 𝑑 + 1 𝐸 𝑣 2 1 1 + 𝜏 2 πœ• 𝑑 ξ‚Ά 𝜎 ; the differential operator πœ• 𝑑 ≑ πœ• / πœ• 𝑑

        Viscoelastic Operator that Corresponds to the Modulus of Elasticity 𝐸
                 1 𝐸 β†’ 1 πœ‚ 1 πœ• 𝑑 + 1 𝐸 𝑣 2 1 1 + 𝜏 2 πœ• 𝑑

              The modified Creep Model
          𝑒 ( 𝑑 ) β„Ž 0 = βŽ› ⎜ ⎜ ⎝ 𝑏 πœ’ πœ‚ 1 πœ‚ 2 𝑃 0 𝐿 0 ( πœ‚ 1 + πœ‚ 2 ) ⎞ ⎟ ⎟ ⎠ 1 / ( πœ’ + 1 ) 𝑑 1 / ( πœ’ + 1 ) Ξ“ ( ( πœ’ + 2 ) / ( πœ’ + 1 ) ) Γ— Ξ¦ 2 βŽ› ⎜ ⎜ ⎝ βˆ’ 1 πœ’ + 1 , 1 πœ’ + 1 ; πœ’ + 2 πœ’ + 1 , βˆ’ 𝑑 𝜏 2 , βˆ’ 𝐸 𝑣 2 πœ‚ 1 + πœ‚ 2 𝑑 ⎞ ⎟ ⎟ ⎠ ,
     where Ξ¦ 2 is the confluent hypergeometric function of two variables (Appell function)
              which is defined by:
           Ξ¦ 2 βˆ‘ ( 𝛼 , 𝛽 , 𝛾 , π‘₯ , 𝑦 ) = ∞ π‘š = 0 βˆ‘ ∞ 𝑛 = 0 ( 𝛼 ) π‘š ( 𝛽 ) 𝑛 ( 𝛾 ) π‘š + 𝑛 π‘₯ π‘š 𝑦 𝑛 π‘š ! 𝑛 !
     where ( π‘Ž ) π‘˜ is Pochhammer's notation, that is, ( π‘Ž ) 0 = 1 , ( π‘Ž ) 1 = π‘Ž , ( π‘Ž ) π‘˜ = ( π‘Ž ) π‘˜ βˆ’ 1 ( π‘Ž + π‘˜ βˆ’ 1 )