We consider a commutative algebra over the field of complex numbers with a basis {e1, e2}
satisfying the conditions,. Let D be a bounded domain in the Cartesian plane xOy and …

In this paper, an analog of the conformable fractional derivative is defined in an arbitrary
finite-dimensional commutative associative algebra. Functions taking values in the indicated …

The idea of an algebraic-analytic approach to equations of mathematical physics means to
find a commutative Banach algebra such that monogenic functions with values in this …

In [2], a method for the formal construction of solutions of the three-dimensional Laplace
equation is developed by using power series in any harmonic algebra over the field of …

We develop a hypercomplex method of solving of boundary value problems for biharmonic
functions. This method is based on a relation between biharmonic functions and monogenic …

We consider a commutative algebra 𝔹 over the field of complex numbers with a basis {e 1, e
2} satisfying the conditions (e 1 2+ e 2 2) 2= 0, e 1 2+ e 2 2≠ 0. Let D be a bounded simply …

The methods involving the functions analytic in a complex plane for plane potential fields
inspire the search for the analogous efficient methods for solving the spatial and …

We consider a two-dimensional commutative algebra B over the field of complex numbers.
The algebra B is associated with the biharmonic equation. For monogenic functions with …

Consider the commutative algebra $\mathbb {B} $ over the field of complex numbers with
the bases $\{e_1, e_2\} $ such that% satisfying the conditions $(e_1^ 2+ e_2^ 2)^ 2= 0 …

For an algebra B 0≔ c 1 e+ c 2 ω: ck∈ ℂ k= 1 2 B _0:=\left {c _1e+ c _2 ω: c _k ∈ C, k= 1,
2\right\}, e 2= ω 2= e, eω= ωe= ω, over the field of complex numbers ℂ, we consider arbitrary …