Nonexistence of global solutions to a hyperbolic equation with a space–time fractional damping

Nonexistence of Global Solutions to Higher-Order Time-Fractional Evolution Inequalities with Subcritical Degeneracy

“…Finally, using (12), and letting T → ∞ into the above inequality, we obtain R N F(x)|x| −ν dx ≤ 0, which contradicts the condition R N F(x)|x| −ν dx > 0. The proof of Theorem 2 is completed.…”

“…Due to the usefulness of fractional derivatives in modeling various phenomena from science and engineering (as can be seen in, e.g., [6][7][8][9]), the study of fractional partial differential equations (as well as fractional differential equations) becomes a subject of increasing concern. The study of the nonexistence of global solutions to time-fractional evolution equations and inequalities has been initiated by Kirane and their collaborators (as can be seen in, e.g., [10][11][12][13][14]). In particular, in [13], Kirane et al studied the nonexistence of nontrivial global weak non-negative solutions to the fractional-in-time and in-space evolution equation:…”

Nonexistence of Global Weak Solutions of a System of Nonlinear Wave Equations with Nonlinear Fractional Damping

“…Before we state and prove our result, let us dwell on existence literature. Single wave equations or systems of wave equations have been studied in large; we may mention the books of Lions [2], Reed [3], Georgiev [4], and Strauss [5] and the papers of Aliev et al [6], Said-Houari [7], Takeda [8], Goergiev and Todorova [9], Todorova and Yordanov [10], Zhang [11], and Kirane and Qafsaoui [12] for equations and systems with classical linear or nonlinear damping and Tatar [13], Kirane and Tatar [14], and Kirane and Laskri [15] for wave equations with fractional damping. In particular, in [13], the following problem was considered:…”

“…Namely, it was shown that the solution of ( 2) is unbounded and grows up exponentially in the L p+1 -norm for sufficiently large initial data. In [15], the following problem was studied:…”

A note on fractional parabolic differential and difference equations

“…Theory and numerical methods of initial-boundary value problems for fractional parabolic equations were investigated by many researchers (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][22][23][24] and the references given therein). In this paper, the initial-boundary value problem for the multidimensional fractional parabolic equation…”