"We study the well-posedness for solutions of an initial-value boundary
problem on a two-dimensional space with source functions associated to
nonlinear fractional di usion equations with the Riemann-Liouville derivative
and nonlinearities with memory on a two-dimensional domain. In order to
derive the existence and uniqueness for solutions, we mainly proceed on reasonable
choices of Hilbert spaces and the Banach xed point principle. Main
results related to the Mittag-Le er functions such as its usual lower or upper
bound and the relationship with the Mainardi function are also applied. In
addition, to set up the global-in-time results, Lp Lq estimates and the smallness
assumption on the initial data function are also necessary to be applied in
this research. Finally, the work also considers numerical examples to illustrate
the graphs of analytic solutions"