A quaternionic fractional Borel-Pompeiu type formula

@article{GonzalezCervantes2021AQF,
  title={A quaternionic fractional Borel-Pompeiu type formula},
  author={Jos'e Oscar Gonz'alez-Cervantes and Juan Bory-Reyes},
  journal={Fractals},
  year={2021}
}
In theoretical setting, associated with a fractional ψ−Fueter operator that depends on an additional vector of complex parameters with fractional real parts, this paper establishes a fractional analogue of Borel-Pompeiu formula as a first step to develop a fractional ψ−hyperholomorphic function theory and the related operator calculus. 
A fractional Borel-Pompeiu type formula for holomorphic functions of two complex variables
The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ψ−Fueter operator in the one-dimensional Riemann–Liouville derivativeExpand
A quaternionic perturbed fractional $\psi-$Fueter operator calculus
Quaternionic analysis offers a function theory focused on the concept of ψ−hyperholomorphic functions defined as null solutions of the ψ−Fueter operator, where ψ is an arbitrary orthogonal baseExpand

References

SHOWING 1-10 OF 43 REFERENCES
A higher dimensional fractional Borel‐Pompeiu formula and a related hypercomplex fractional operator calculus
In this paper we develop a fractional integro-differential operator calculus for Clifford-algebra valued functions. To do that we introduce fractional analogues of the Teodorescu and Cauchy-BitsadzeExpand
Higher order Borel–Pompeiu representations in Clifford analysis
In this paper, we show that a higher order Borel–Pompeiu (Cauchy–Pompeiu) formula, associated with an arbitrary orthogonal basis (called structural set) of a Euclidean space, can be extended to theExpand
Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems II. algebras of singular lntegral operators and riemann type boundary value problems
We study some algebras generated by the singular integral operator with the quaternionic Cauchy kernel and the multiplication operators by continuous or piece-wise continuous functions. This allowsExpand
Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense
In this paper, we present the development of fractional bicomplex calculus in the Riemann–Liouville sense, based on the modification of the Cauchy–Riemann operator using the one-dimensionalExpand
A class of time-fractional Dirac type operators
Abstract By using a Witt basis, a new class of time-fractional Dirac type operators with time-variable coefficients is introduced. These operators lead to considering a wide range of fractionalExpand
Quaternionic and Clifford Calculus for Physicists and Engineers
Quanternions and Multivectors. Clifford Valued Functions and Forms. Clifford Operator Calculus. Boundary Value Problems. Numerical Clifford Analysis. Further Results and Research Problems.Expand
Fischer Decomposition and Cauchy–Kovalevskaya Extension in Fractional Clifford Analysis: The Riemann–Liouville Case
  • N. Vieira
  • Mathematics
  • Proceedings of the Edinburgh Mathematical Society
  • 2016
Abstract In this paper we present the basic tools of a fractional function theory in higher dimensions by means of a fractional correspondence to the Weyl relations via fractional Riemann–LiouvilleExpand
Differentiation of the Martinelli‐Bochner Integrals and the Notion of Hyperderivability
The notion of hyperderivability is introduced and discussed which allows us to obtain, in particular, formulas for the derivatives of the Martinelli-Bochner integrals.
A Fractional Dirac Operator
Based on the Riesz potential, S. Samko and coworkers studied the fractional integro-differentiation of functions of many variables which is a fractional power of the Laplace operator. We will extendExpand
Integral Representations For Spatial Models of Mathematical Physics
Introduction and some remarks on generalisations of complex analysis a-holomorphic function theory Electrodynamical models Massive spinor fields Hypercomplex factorization, systems of non-linearExpand
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