Local Well-posedness of Nonlinear Time–fractional Diffusion Equation

Apassara Suechoei, Parinya Sa Ngiamsunthorn


We study the local well-posedness of the following time-fractional nonlinear diffusion equation

where and denotes Caputo tempered fractional derivative of order . The local existence and uniqueness results are obtained from heat kernel and fixed point theorem. Then, we extend the solution to establish a maximal mild solution. Moreover, we provide estimate for continuous dependence on initial condition.

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|ISSN 1686-0209|