On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition

The aim of this paper is to investigate the existence of mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition. Unlike previous papers, in the current paper, we assume that the source function of the problem may have a singularity. The existence results are proven via the Schaefer, nonlinear Leray–Schauder alternatives and Banach fixed point theorems. Further, the continuity of mild solutions in terms of inputs (fractional orders, nonlocal condition, and associated parameters) is extensively discussed.