Hmissi, Mohamed; Mejri, Hassen; Mliki, Ezeddine On the fractional powers of semidynamical systems. (English) Zbl 1152.45005 Grazer Math. Ber. 351, 66-78 (2007). The authors investigate the following functional equation \[ \int_0^{\infty}f(s, \Phi(r,x))\eta_t^{\alpha}(dr)=f(s+t,x), \quad x,t\in\mathbb R^{+},\;x\in E, \] in which \(\Phi\) is a semidynamical system with state space \(E\) and \(\eta^{\alpha}=(\eta_t^{\alpha})_{(t>0)}\). They find that its solution \(f(s,t): (0,\infty)\times E\to [0,\infty)\), is the fractional power convolution semigroup of order \(\alpha\in(0,1)\). They also show that the considered equation relates to the so-called \(\alpha\)-Lyapunov functions defined by \(\Phi\) and \(\eta^{\alpha}\). Reviewer: Changpin Li (Shanghai) Cited in 1 Document MSC: 45G05 Singular nonlinear integral equations 26A33 Fractional derivatives and integrals 37B25 Stability of topological dynamical systems Keywords:semidynamical system; fractional power subordinator; exit equation; nonlinear singular integral equation PDFBibTeX XMLCite \textit{M. Hmissi} et al., Grazer Math. Ber. 351, 66--78 (2007; Zbl 1152.45005)