Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart hyper-Bessel operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansion and results on existence and uniqueness are established. To solve the resultant equations, a solution to a non-homogeneous fractional differential equation with regularized Caputo-like counterpart hyper-Bessel operator is also presented.