This paper addresses the existence and uniqueness of mild solutions to the Navier–Stokes
equations with time fractional differential operator of order α∈(0, 1). Several interesting …

We consider non-linear time-fractional stochastic heat type equation∂ t β ut (x)=− ν (− Δ) α/2
ut (x)+ I t 1− β [σ (u) W⋅(t, x)] in (d+ 1) dimensions, where ν> 0, β∈(0, 1), α∈(0, 2] and d< …

The 20th century was rich with great scientific and mathematical discoveries. One of the
most influential events in mathematics was the introduction of the Lebesgue integral …

The dual-phase-lag model provides the best performance among many existing non-Fourier
models and it is particularly more suitable for a short duration of heating. The present …

Consider non-linear time-fractional stochastic heat type equations of the following type, ∂^
β _tu_t (x)=-ν (-Δ)^ α/2 u_t (x)+ I^ 1-β _t λ σ (u) F\limits^ ⋅ (t, x)∂ t β ut (x)=-ν (-Δ) α/2 ut (x)+ I t …

Water injection can result in the creation of induced fracture by connecting natural fractures.
The induced fracture penetrates the entire reservoir, leading to the interconnection of …

Abstract Systems of fractional order differential and pseudo-differential equations are used
in modeling of various dynamical processes. In the analysis of such models, including …

In this paper, we study existence and uniqueness of strong as well as weak solutions for
general time fractional Poisson equations. We show that there is an integral representation …

We consider a diffusion equation involving fractional derivative in time of order β (0< β< 1)
with a nonlocal boundary condition involving a parameter α> 0. A bi-orthogonal system of …

This paper studies the Galerkin finite element approximations of a class of stochastic
fractional differential equations. The discretization in space is done by a standard …