On the solutions of time-fractional reaction–diffusion equations

Uniqueness for an inverse problem for a semilinear time-fractional diffusion equation

“…Additional condition is given in a form of an integral with Borel measure over the time that includes as a particular case the final overdetermination. Such an inverse problem has possible applications in modelling of fractional reaction-diffusion processes [5,12,23], more precisely in reconstruction of certain parameters of inhomogeneous media.…”

Numerical algorithms for multidimensional time-fractional wave equation of distributed-order with a nonlinear source term

“…When considering the high-dimensional models, Gao et al investigated ADI schemes for two-dimensional distributed-order diffusion equations [20] [21], and they also developed two ADI difference schemes for solving the two-dimensional time distributed-order wave equations [22]. Due to the widespread use of the nonlinear models [23] [24], M. L. Morgado et al developed an implicit difference scheme for one-dimensional time distributed-order diffusion equation with a nonlinear source term [25]. For further discussion on the numerical approaches for solving the high-dimensional distributed-order partial differential equations, this paper is devoted to develop effective numerical algorithm for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term…”

Boundary feedback stabilisation for the time fractional‐order anomalous diffusion system

“…Here (1) can be viewed as a model of a thin rod with not only the heat loss to a surrounding medium, but also the heat generation inside the rod in a spatially inhomogeneous environment. For more information on fractional reaction-diffusion equations, we refer the readers to [29][30][31][32] and the reference therein. When α = 1, the problem (1) is reduced to the classical integerorder unstable heat equation.…”