Table 2: Kelvin-Voigt viscoelastic medium.

              Model Constitutive equation
        𝜎 𝜀 = 𝐸 𝑒 + 𝜂 𝜕 𝑡 ; the differential operator 𝜕 𝑡 𝜕 / 𝜕 𝑡

        Viscoelastic Operator that Corresponds to the Modulus of Elasticity 𝐸
                1 𝐸 1 𝐸 𝑒 1 1 + 𝜏 𝜕 𝑡

              The modified Creep Model
   𝑢 ( 𝑡 ) 0 = 1 Γ ( ( 2 + 𝜒 ) / ( 1 + 𝜒 ) ) 𝑏 𝜒 𝜏 𝐸 𝑒 𝐹 0 𝐿 0 1 / ( 𝜒 + 1 ) 𝜏 ( 2 + 𝜒 ) / 2 ( 1 + 𝜒 ) × 𝑡 𝜒 / 2 ( 1 + 𝜒 ) 𝑒 𝑡 / 2 𝜏 𝑀 𝜒 / 2 ( 1 + 𝜒 ) , 1 / 2 ( 1 + 𝜒 ) [ 𝑡 / 𝜏 ] ,
 where Γ is the gamma function, 𝑀 𝜇 , 𝜈 ( 𝑥 ) is the Whittaker’s hypergeometric function and equals to:
𝑀 𝜇 , 𝜈 ( 𝑥 ) = 𝑥 1 / 2 + 𝜈 𝑒 𝑥 / 2 × 1 𝐹 1 1 2 + 𝜈 𝜇 ; 2 𝜈 + 1 ; 𝑥 and 1 𝐹 1 [ 𝑐 ; 𝑑 ; 𝑥 ] is the Kummer’s confluent
 hypergeometric function which could be expressed as 1 𝐹 1 [ 𝑐 ; 𝑑 ; 𝑥 ] = 𝑛 = 0 ( 𝑐 ) 𝑛 ( 𝑑 ) 𝑛 𝑥 𝑛 𝑛 ! , or:
1 𝐹 1 𝑐 [ 𝑐 ; 𝑑 ; 𝑥 ] = 1 + 𝑑 𝑥 + 𝑐 ( 𝑐 + 1 ) 𝑥 2 + 𝑑 ( 𝑑 + 1 ) 2 ! 𝑐 ( 𝑐 + 1 ) ( 𝑐 + 2 ) 𝑥 3 𝑑 ( 𝑑 + 1 ) ( 𝑑 + 2 ) 3 ! +

              The modified Thermal Creep Model
     𝑢 ( 𝑡 ) 0 = 𝑏 𝜒 𝜏 𝐸 𝑒 𝑃 0 𝐿 0 1 / ( 𝜒 + 1 ) 𝑡 1 / ( 1 + 𝜒 ) Γ ( ( 2 + 𝜒 ) / ( 1 + 𝜒 ) ) 1 𝐹 1 1 ; 1 + 𝜒 2 + 𝜒 𝑡 1 + 𝜒 ; 𝜏 𝑄 × e x p 𝑅 1 𝑇 1 𝑇 0