Fractional differential equations (FDES), ie, differential equations involving fractional-order
derivatives, have received much recent attention in engineering, physics, biology and …

In this paper, we review some results over the last 10-15 years on elliptic and parabolic
equations with discontinuous coefficients. We begin with an approach given by NV Krylov to …

In this paper, we consider traces at initial times for functions with mixed time‐space
smoothness. Such results are often needed in the theory of evolution equations. Our result …

The L-fractional derivative is defined as a certain normalization of the well-known Caputo
derivative, so alternative properties hold: smoothness and finite slope at the origin for the …

This article aims to investigate the semi-classical analog of the general Caputo-type
diffusion equation with time-dependent diffusion coefficient associated with the discrete …

We obtain L p estimates for fractional parabolic equations with space-time non-local
operators∂ t α uL u+ λ u= f in (0, T)× R d, where∂ t α u is the Caputo fractional derivative of …

This paper is a comprehensive study of L p estimates for time fractional wave equations of
order α∈(1, 2) in the whole space, a half space, or a cylindrical domain. We obtain weighted …

In this study, we investigate the existence, uniqueness, and maximal regularity estimates of
solutions to homogeneous initial value problems involving time-measurable pseudo …

We consider time fractional parabolic equations in divergence and non-divergence form
when the leading coefficients are measurable functions of except for, which is a measurable …

This paper considers traces at the initial time for solutions of evolution equations with local
or non-local derivatives in vector-valued $ L_p $ spaces with $ A_p $ weight. To achieve …