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< …

In this paper diffusion processes with changing modes are studied involving the variable
order partial differential equations. We prove the existence and uniqueness theorem of a …

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 …

Abstract top 2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10,
86A05Fractional diffusion equations are abstract partial differential equations that involve …

We study the nonlinear stochastic time-fractional diffusion equations in the spatial domain
$\mathbb {R} $, driven by multiplicative space-time white noise. The fractional index $\beta …

This book is an unique integrated treatise, on the concepts of fractional calculus as models
with applications in hydrology, soil science and geomechanics. The models are primarily …

The classical Duhamel principle, established nearly 200 years ago by Jean-Marie-Constant
Duhamel, reduces the Cauchy problem for an inhomogeneous partial differential equation to …

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 …

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 …

The paper is a new approach to the Duhamel integral. It contains an overview of formulas
and applications of Duhamel's integral as well as a number of new results on the Duhamel …