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.
This work was done during the visit of authors to ICMS in Edinburgh in July 2016 and was supported by “Research in Group” activity of ICMS. The last author was also supported in part by the EPSRC grant EP/K039407/1 and by the Leverhulme Grant RPG-2014-02.
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