m-MP-weak Drazin matrices

The concepts of Moore–Penrose weak Drazin (MP-w-D) and weak Drazin Moore–Penrose (w-D-MP) matrices are defined based on the Moore–Penrose inverse in combination with a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse. By using the [Formula: see text]th powers of a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse instead of a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse, we generalize the notions of MP-w-D and w-D-MP matrices and present the [Formula: see text]-MP-w-D and [Formula: see text]-w-D-MP matrices as new classes of square matrices. Recently considered [Formula: see text], [Formula: see text], MP-w-D and w-D-MP matrices are special types of [Formula: see text]-MP-w-D and [Formula: see text]-w-D-MP matrices and we study wider classes of matrices. We verify many characterizations and representations of our new types of matrices. New particular kinds of [Formula: see text]-MP-w-D and [Formula: see text]-w-D-MP matrices are investigated too. By applying the [Formula: see text]-MP-w-D and [Formula: see text]-w-D-MP matrices, we solve several linear equations.