Fractional Fischer decompositions by inframonogenic functions

Inframonogenic functions can be viewed as a non -commutative version of the more traditional harmonic functions. In this paper we obtain a new Fischer decomposition for homogeneous polynomials in R m in terms of ( phi, psi )-inframonogenic homogeneous polynomials. The latter being a natural generalization arising when structural sets phi , psi are considered instead of the standard orthonormal basis of R m . Moreover, we extend our results to the fractional context by means of the Caputo derivative and Weyl relations. (c) 2024 Elsevier Inc. All rights reserved.