WELL-POSEDNESS RESULTS FOR NONLINEAR FRACTIONAL DIFFUSION EQUATION WITH MEMORY QUANTITY

We study the well-posedness for solutions of an initial-value bound-ary problem on a two-dimensional space with source functions associated to nonlinear fractional diffusion 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 rea-sonable choices of Hilbert spaces and the Banach fixed point principle. Main results related to the Mittag-Leffler 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 small-ness 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.