Fractional calculus has been applied to signal and image processing for almost two decades. For instance, it was successfully used for noise filtering and pattern recognition. Some books on this topic are:

Ostalczyk, P. Discrete Fractional Calculus: Applications In Control And Image Processing (Series In Computer Vision Book 4), World Scientific, 2015.

Das, S., Pan, I. Fractional Order Signal Processing: Introductory Concepts and Applications (SpringerBriefs in Applied Sciences and Technology), Springer, 2012.

Sheng, H., Chen, YQ, Qiu, TS. Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications (Signals and Communication Technology), Springer, 2012.

Cabral, T.M., Rangayyan, R.M. Fractal Analysis of Breast Masses in Mammograms (Synthesis Lectures on Biomedical Engineering), Morgan & Claypool Publishers, 2012.

Fractional calculus has also been applied to neural networks, machine learning and artificial intelligence.

Here some applications

Article Adaptive fractional differential approach and its applicatio...

Article Fractional Order Image Processing of Medical Images

I concur with V.V. Smirnov