On the fractional Cornu spirals

•Generalisation of Cornu spirals in the perspective of fractional calculus.•Calculation of fractional Cornu spirals.•Use of symbolic packages in fractional calculus. This paper introduces two fractional integral sine and cosine curves. Based on such formulation a series of fractional plane and space Cornu spirals are represented. These curves can be used for modeling diffraction phenomena under the light of the fractional calculus tools. The adoption of symbolic packages simplifies the model implementation showing that present-day computational resources lead to a straightforward implementation of fractional differential equations.