Abstract
Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.
Acknowledgements
Authors would like to thank Prof. V. Kiryakova for her valuable comments and suggestions. Authors also acknowledge financial support from the Research Council (TRC), Oman. This work is funded by TRC under the research agreement No. ORG/SQU/CBS/13/030.
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