Hypercomplex operator calculus for the fractional Helmholtz equation

DOI10.1002/mma.10064MaRDI QIDQ6619369

Milton Ferreira, Rolf Sören Krausshar, M. Manuela Rodrigues, Nelson Vieira

Publication date: 15 October 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

fundamental solutionsfractional derivativesseparation of variablessteady-state oscillationsStokes formulaBorel-Pompeiu formulafractional Clifford analysisfractional Helmholtz equationsLeray-Hodge decompositionspatial blow-ups

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Functions of hypercomplex variables and generalized variables (30G35) Fundamental solutions to PDEs (35A08) Fractional derivatives and integrals (26A33) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral operators (45P05) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hodge-type decomposition for time-dependent first-order parabolic operators with non-constant coefficients: the variable exponent case
• Hodge decomposition and solution formulas for some first-order time-dependent parabolic operators with non-constant coefficients
• Hodge type decomposition in variable exponent spaces for the time-dependent operators: the Schrödinger case
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• A time-fractional Borel-Pompeiu formula and a related hypercomplex operator calculus
• A practical guide to Prabhakar fractional calculus
• On the fractional derivative of Dirac delta function and its application
• Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case
• Exact solutions of the 3D fractional Helmholtz equation by fractional differential transform method
• A function theory for the operator D-λ
• A higher dimensional fractional Borel‐Pompeiu formula and a related hypercomplex fractional operator calculus
• Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives
• Mittag-Leffler Functions, Related Topics and Applications

This page was built for publication: Hypercomplex operator calculus for the fractional Helmholtz equation