Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator

Fractional Dzherbashian-Nersesian operator is considered and three famous fractional order derivatives named after Riemann-Liouville, Caputo and Hilfer are shown to be special cases of the earlier one. The expression for Laplace transform of fractional Dzherbashian-Nersesian operator is constructed. Inverse problems of recovering space dependent and time dependent source terms of a time fractional diffusion equation with involution and involving fractional Dzherbashian-Nersesian operator are considered. The results on existence and uniqueness for the solutions of inverse problems are established. The results obtained here generalize several known results.