Abstract
We present a generalization of several results of the classical continuous Clifford function theory to the context of fractional Clifford analysis. The aim of this paper is to show how the fractional integro-differential hypercomplex operator calculus can be applied to a concrete fractional Stokes problem in arbitrary dimensions which has been attracting recent interest (cf. [1, 6]).
Highlights
To explicitly describe the integral kernels that are used in the sequel we need to introduce the two-parameter
Recalling from [2] we know that a family of fundamental solutions of the fractional Dirac operator CDaα+
For all the detailed proofs and calculations we refer to our paper [2]
Summary
B ∈ R with a < b and α > 0, the left and right Riemann-Liouville fractional integrals Iaα+ and Ibα− of order α are defined by (see [5]). By RLDaα+ and RLDbα− we denote the left and right Riemann-Liouville fractional derivatives of order α > 0 on [a, b] ⊂ R (see [5]): RLDaα+ f (x) =. Right) Caputo fractional derivative of order α > 0: CDaα+ f. The n-parameter fractional Laplace operators RL∆αa+ and C∆αa+ , and the associated fractional Dirac operators RLDaα+ and CDaα+ acting on the variables (x1, · · · , xn) ∈ Rn are defined over Ω by n. 1+αi xi 2 are the left Riemann-Liouville and Caputo fractional derivatives and of orders. The functions v and vx are defined in Corollary 3.5 of [2]
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