This paper presents a fractional drift-diffusion (Fr-DD) model to characterize the transconductance characteristics of a 6,13-bis(triisopropylsilylethynyl)pentacene TIPS-pentacene based organic field effect transistor (OFET) when bending effects are taken into account. The Fr-DD model is proposed by fractionalizing the diffusive current density in the carrier continuity equations of the conventional drift-diffusion (DD) model. Gummel’s iteration is utilized to decouple the governing equations of the Fr-DD model. The solved hole concentration and electrostatic potentials on the metal-semiconductor interface are employed to approximate the terminal current flow and generate the transconductance characteristics of the OFET. Compared to the conventional DD model, the Fr-DD model does not need to consider the density of trap states (DoS) since its fractional derivative order in relation to material type, boundary conditions and bending radius can be obtained directly by fitting limited experimental data. In addition, a comparison with experimental data reveals that the Fr-DD model can result in much more accurate predictions on transconductance characteristics than the conventional DD model, especially in the subthreshold and low gate-source voltage regions of the OFET.