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The convolution quadrature method originally developed for theRiemann-Liouville fractional calculus is extended in this work to the Hadamardfractional calculus by using the exponential type meshes. Local truncationerror analysis is presented for singular solutions. By adopting the fractionalBDF-$p(1\leq p \leq 6)$ for the Caputo-Hadamard fractional derivative insolving subdiffusion problem with singular source terms, and using the finiteelement method to discretize the space variable, we carry out the sharp erroranalysis rigorously and obtain the optimal accuracy by the novel correctiontechnique. Our correction method is a natural generalization of the onedeveloped for subdiffusion problems with smooth source terms. Numerical testsconfirm the correctness of our theoretical results.

Convolution quadrature for Hadamard fractional calculus and correction methods for the subdiffusion with singular source terms