Geodesic
Blow Up Results for Fractional Differential Equations and Systems
Publications de l'Institut Mathématique, _N_S_93 (2013) no. 107, p. 173

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The aim of this research paper is to establish sufficient conditions for the nonexistence of global solutions for the following nonlinear fractional differential equation \begin{gather*} \mathbf{D}_{0|t}^{lpha}u+(-elta)^{\beta/2}|u|^{m-1}u+a(x)\cdotabla|u|^{q-1}u=h(x,t)|u|^p,\;\;(t,x)ı Q, u(0,x)=u_0(x),\;\;xı\R^N \end{gather*} where $(-elta)^{\beta/2}$, $0\beta2$ is the fractional power of $-elta$, and $\mathbf{D}_{0|t}^{\alpha}$, $(0\alpha1)$ denotes the time-derivative of arbitrary $\alpha\in(0;1)$ in the sense of Caputo. The results are shown by the use of test function theory and extended to systems of the same type.
Classification : 58J45 26A33 35B44
Keywords: blow-up, fractional derivatives, critical exponent 
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     author = {Ali Hakem and Mohamed Berbiche},
     title = {Blow {Up} {Results} for {Fractional} {Differential} {Equations} and {Systems}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {173 },
     publisher = {mathdoc},
     volume = {_N_S_93},
     number = {107},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2013_N_S_93_107_a14/}
}
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Ali Hakem; Mohamed Berbiche. Blow Up Results for Fractional Differential Equations and Systems. Publications de l'Institut Mathématique, _N_S_93 (2013) no. 107, p. 173 . http://geodesic.mathdoc.fr/item/PIM_2013_N_S_93_107_a14/