We study travelling-wave solutions of the generalized Sharma-Tasso-Olver (GSTO) equation $u_t+\lambda(u^{r})_x+\mu(u^{s})_{xx}+\nu u_{xxx}=0$, in which the exponents $r,s>0$ need not be integers. The classical, modified and generalized Kudryashov methods are applied to the reduced ordinary differential equation. A balance argument shows that the convective term fixes the degree of the expansion through $N=2/(r-1)$, whereas the nonlinear diffusion term requires $N=1/(s-1)$; the two requirements are compatible only when $r=2s-1$, a condition satisfied by the classical STO equation ($r=3$, $s=2$). For the representative non-integer cases $(r,s)=(2,\tfrac32)$ and $(\tfrac32,2)$ we show that boun... More >