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Direct and inverse source problems of a fractional diffusion equation withregularized Caputo-like counterpart hyper-Bessel operator are considered.Solutions to these problems are constructed based on appropriate eigenfunctionexpansion and results on existence and uniqueness are established. To solve theresultant equations, a solution to a non-homogeneous fractional differentialequation with regularized Caputo-like counterpart hyper-Bessel operator is alsopresented.

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