Global and local existence of solution for fractional heat equation in $\mathbb{R}^N$ by Balakrishnan definition
Mathematica Moravica, Tome 26 (2022) no. 1.

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

Our aim here is to collect and to compare two definitions of the fractional powers of non-negative operators that can be found in the literature; we will present the proof of an equivalence and compare properties of that notions in different approaches. Then we will apply next this equivalence in the study of global and local existence of solution for the semilinear Cauchy problem in $\R^N$ with fractional Laplacian \[ eft\{ \begin{array}{c} u_t = -(-\Delta)^lpha u + f(x,u), u(0,x) = u_0(x), \quad x ı \R^N. \end{array} \right. \]
Mots-clés : Fractional powers of operator, Balakrishinan, global solvability, Heat Equation. 
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     author = {Jorge Ferreira and Erhan Pi\c{s}kin and Mohammad Shahrouzi and Sebasti\~ao Cordeiro and Daniel Rocha},
     title = {Global and local existence of solution for fractional heat equation in $\mathbb{R}^N$ by {Balakrishnan} definition},
     journal = {Mathematica Moravica},
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Jorge Ferreira; Erhan Pişkin; Mohammad Shahrouzi; Sebastião Cordeiro; Daniel Rocha. Global and local existence of solution for fractional heat equation in $\mathbb{R}^N$ by Balakrishnan definition. Mathematica Moravica, Tome 26 (2022) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2022_26_1_a6/