On a class of semilinear nonclassical fractional wave equations with logarithmic nonlinearity

In this paper, we consider the initial boundary value problem for time‐fractional subdiffusive equations with Caputo derivative. Our problem has many applications in population dynamics. The source function is given in the logarithmic form. We examine the existence, uniqueness of local solutions, and their ability to continue to a maximal interval of existence. The main tool and analysis here are of applying some Sobolev embedding and some fixed point theorems.