On time-fractional partial differential equations of time-dependent piecewise constant order

This contribution considers the time-fractional subdiffusion with a time-dependent variable-order fractional operator of order β(t). It is assumed that β(t) is a piecewise constant function with a finite number of jumps. A proof technique based on the Fourier method and results from constant-order fractional subdiffusion equations has been designed. This novel approach results in the well-posedness of the problem.