Open AccessPosted Content
A quaternionic fractional Borel-Pompeiu type formula
TLDR
In this article, a fractional analogue of Borel-Pompeiu formula is established as a first step to develop fractional $\psi-$hyperholomorphic function theory and the related operator calculus.Abstract:
Quaternionic analysis relies heavily on results on functions defined on domains in $\mathbb R^4$ (or $\mathbb R^3$) with values in $\mathbb H$. This theory is centered around the concept of $\psi-$hyperholomorphic functions i.e., null-solutions of the $\psi-$Fueter operator related to a so-called structural set $\psi$ of $\mathbb H^4$. Fractional calculus, involving derivatives-integrals of arbitrary real or complex order, is the natural generalization of the classical calculus, which in the latter years became a well-suited tool by many researchers working in several branches of science and engineering. In theoretical setting, associated with a fractional $\psi-$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 $\psi-$hyperholomorphic function theory and the related operator calculus.read more
Citations
More filters
Posted Content
A quaternionic perturbed fractional $\psi-$Fueter operator calculus
TL;DR: In this article, a quaternionic perturbed fractional $\psi-$Fueter operator calculus is introduced, where Stokes and Borel-Pompeiu formulas in this perturbation are presented.
References
More filters
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
TL;DR: In this article, the authors present a method for computing fractional derivatives of the Fractional Calculus using the Laplace Transform Method and the Fourier Transformer Transform of fractional Derivatives.
Book
The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order
Keith B. Oldham,Jerome Spanier +1 more
TL;DR: In the beginning, when having significantly cash, why don't you attempt to acquire something basic in the beginning? That's something that will guide you to understand even more in the region of the globe, experience, some places, history, amusement, and a lot more as discussed by the authors.
Book
Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media
TL;DR: In this article, the Ginzburg-Landau Equation for Fractal Media and Fokker-Planck Equation of Fractal Distributions of Probability are presented.
Book
Fractional Calculus for Scientists and Engineers
TL;DR: This book gives a practical overview of Fractional Calculus as it relates to Signal Processing in the context of Signal Processing.