Fischer Decomposition and Cauchy–Kovalevskaya Extension in Fractional Clifford Analysis: The Riemann–Liouville Case

DOI10.1017/S0013091516000109zbMath1364.30059MaRDI QIDQ2976363

Nelson Vieira

Publication date: 28 April 2017

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Fischer decompositionfractional monogenic functionsAlmansi decompositionfractional Clifford analysis

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Fractional derivatives and integrals (26A33)

Related Items (14)

A class of time-fractional Dirac type operators ⋮ Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case ⋮ A QUATERNIONIC FRACTIONAL BOREL–POMPEIU-TYPE FORMULA ⋮ Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators ⋮ Fischer decomposition in generalized fractional ternary Clifford analysis ⋮ Homogeneous \((\alpha,k)\)-polynomial solutions of the fractional Riesz system in hyperbolic space ⋮ A FRACTIONAL BOREL–POMPEIU-TYPE FORMULA FOR HOLOMORPHIC FUNCTIONS OF TWO COMPLEX VARIABLES ⋮ The Atiyah-Singer index theorem for a family of fractional Dirac operators on spin geometry ⋮ A fractional Borel–Pompeiu type formula and a related fractional ψ−$$ \psi - $$Fueter operator with respect to a vector‐valued function ⋮ Fractional slice regular functions of a quaternionic variable ⋮ Generalized fractional Cauchy-Riemann operator associated with the fractional Cauchy-Riemann operator ⋮ Fischer Decomposition in Generalized Fractional Clifford Analysis ⋮ Fractional elementary bicomplex functions in the Riemann-Liouville sense ⋮ Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense

Cites Work

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• Cauchy-Kowalevski extensions and monogenic plane waves using spherical monogenics
• The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator
• The Cauchy-Kovalevskaya extension theorem in Hermitian Clifford analysis
• Fractional Dirac operators and deformed field theory on Clifford algebra
• The Cauchy-Kovalevskaya extension theorem in discrete Clifford analysis
• Fischer decomposition and Cauchy kernel for Dunkl-Dirac operators
• The Howe duality for the Dunkl version of the Dirac operator
• Fractional vector calculus and fractional Maxwell's equations
• Cauchy-Kovalevskaya extension theorem in fractional Clifford analysis
• Complexity in quantum field theory and physics beyond the standard model
• Fischer decomposition by inframonogenic functions
• Discrete function theory based on skew Weyl relations
• Stirling Numbers and Spin-Euler Polynomials
• Lie superalgebras

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