In this work, we investigate analytically the solutions of a nonlinear div-curl system with
fractional derivatives of the Riemann–Liouville or Caputo types. To this end, the fractional …

We investigate a generalization of the equation curl w→= g→ to an arbitrary number n of
dimensions, which is based on the well-known Moisil–Teodorescu differential operator …

We study the inhomogeneous equation curl w→+ λ w→= g→, λ∈ C, λ≠ 0 over unbounded
domains in R 3, with g→ being an integrable function whose divergence is also integrable …

We construct a one-parameter family of generalized Mathieu functions, which are reduced
quaternion-valued functions of a pair of real variables lying in an ellipse, and which we call λ …

Beltrami fields are complex vector fields FF which satisfy the equation curl F+ λ F= 0. curl F+
λ F= 0. Such fields appear in astrophysics, electromagnetics and plasma physics. We …

In this paper, we present two simple methods for constructing Beltrami fields. The first one
consists of a composition of operators, including a quaternionic transmutation operator as …

In this manuscript, we characterize the kernel of the parabolic Dirac operator in an explicit
way. More precisely, we will show that the members of this kernel equivalently satisfy a …

In this work, we investigate the system formed by the equations div w→= g 0 div\kern0. 3em
w= g _0 and curl w→= g→ curl\kern0. 3em w= g in bounded star‐shaped domains of ℝ 3 R …

Elliptic partial differential equations are important in various areas of mathematical physics.
As examples, we can mention the classical Poisson's and Laplace's equations, as well as …

In this paper, based on a proposed notion of generalized conjugate harmonic pairs in the
framework of complex Clifford analysis, necessary and sufficient conditions for the solvability …