Researchers are becoming increasingly interested in using fractional partial differential equation (FPDE) models for physical systems such as modeling the flow of a gas through porous materials. These models rely on the fraction of the differentiation \(\alpha \) , which needs to be estimated from empirical data. Experimentation is required in order to generate empirical data, specifically, distance x from the pressure source and t the time since the pressure was initially applied to the system which will generate an output pressure measurement p(x, t). While sampling times are easy to choose when a sensor is in place, the location of sensors from the pressure source are typically arbitrarily chosen. This work shows how to design experiments using a sequential design with a base design and sequentially adding sampling design points by finding the optimal sensor locations along x by minimizing A-optimality criteria which is essentially minimizing the of the sum of the marginal variances of all the parameters. To estimate the parameters, a Bayesian framework is utilized combined with a sequential design approach to search through the possible locations for the next sensor in the follow up design. Two simple FPDE parameterizations are used to illustrate the method with an initial sensor location design of six sensors and with five additional sensors locations determined sequentially. The simple examples suggest that the parameter values influence the location of the next best sensor location.