We consider initial value/boundary value problems for fractional diffusion-wave equation:∂ t
α u (x, t)= L u (x, t), where 0< α⩽ 2, where L is a symmetric uniformly elliptic operator with t …

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo
time-fractional derivative where the coefficients are dependent on spatial and time variables …

This research monograph is motivated by problems in mathematical physics that involve
fractional kinetic equations. These equations describe transport dynamics in complex …

We introduce an L q (L p)-theory for the semilinear fractional equations of the type (0.1)∂ t α
u (t, x)= aij (t, x) uxixj (t, x)+ f (t, x, u), t> 0, x∈ R d. Here, α∈(0, 2), p, q> 1, and∂ t α is the …

In this paper, a backward problem for a time–space fractional diffusion equation is
considered, which is to determine the initial data from a noisy final data. To deal with this ill …

We study the regularity of weak solutions to linear time fractional diffusion equations in
divergence form of arbitrary time order α ∈ (0, 1). The coefficients are merely assumed to be …

In this paper we study the time fractional semilinear diffusion equation 0 CD t α u (t, x)− Δ u
(t, x)=| u| p+ t σ w (x) with the initial conditions u (0, x)= u 0 (x) and∂ tu (0, x)= u 1 (x) for x∈ …

In practice many problems related to space/time fractional equations depend on fractional
parameters. But these fractional parameters are not known a priori in modelling problems …

We consider nonlocal in time semilinear subdiffusion equations on a bounded domain,
where the kernel in the integro-differential operator belongs to a large class, which covers …

We prove existence of a bounded weak solution to a degenerate quasilinear subdiffusion
problem with bounded measurable coefficients that may explicitly depend on time. The …