On Existence and Uniqueness of Solution for Space–Time Fractional Zener Model

Mathematical modeling of wave propagation in viscoelastic media with the fractional Zener model

“…We can conclude the proof of surjectivity by showing that, for U = (u, v, s, ϕ) t ∈ D(A) using same step in our work [15].…”

“…The operator A : D(A) ⊂ H −→ H is well defined, it is a bounded operator, we will show it in the same way when the modimensional case (see [15]).…”

“…As in the monodimensional case (see [15]), we write the problem (10) as a first-order evolutionary system using the following auxiliary differential equation [18]:…”

“…Atanackovic et al [7] used the fractional space-time distributional Zener model with the left Riemann-Liouville derivative and the symmetric Caputo derivative for the constraint. In [15] we used semi-group theory to study the existence and uniqueness of the strong solution in space-time for fractional Zener model with the derivative of Caputo. In addition, Atanackovic et al [16] proposed a constitutive equation for a generalized Zener-type viscoelastic body that includes fractional derivatives of stress and strain of real and complex order.…”

A novel higher-order numerical method for parabolic integro-fractional differential equations based on wavelets and $L2$-$1_\sigma$ scheme

“…During the past few decades, the qualitative analysis of fractional differential equations (FDEs) and fractional-order integro-differential equations (FOIDEs) have gained more popularity due to their practical application in numerous fields of science and technology, including control theory [23], cryptography [26], neural networks [20], options trading [11], and viscoelasticity [16], etc. The arbitrary order fractional derivatives, which are nonlocal in nature, are the generalized extension of the classical ones by introducing continuous Gamma functions instead of the discrete factorial functions [22].…”