On boundary-value problems for a partial differential equation with   Caputo and Bessel operators
  In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of solutions to formulated problems in terms of multinomial Mittag-Leffler and first kind Bessel functions. 
Praveen Agarwal, Erkinjon Karimov, Murat Mamchuev, Michael Ruzhansky
math.AP