Axially Symmetric Potentials and Fractional Integration

DOI10.1137/0113014zbMath0158.12504OpenAlexW1981883203MaRDI QIDQ5540760

Arthur Erdélyi

Publication date: 1965

Published in: Journal of the Society for Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0113014

zbMATH Keywords

fractional integrationapplication to solution to boundary value problemAxially symmetric potentials

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Two-dimensional potential theory (31Axx)

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The use of fractional derivatives to expand analytical functions in terms of quadratic functions with applications to special functions ⋮ Decomposition theorem and Riesz basis for axisymmetric potentials in the right half-plane ⋮ A fractional Borel–Pompeiu type formula and a related fractional ψ−$$ \psi - $$Fueter operator with respect to a vector‐valued function ⋮ On differential equations involving the ψ$$ \psi $$‐shifted fractional operators ⋮ On a method for constructing the Riemann function for partial differential equations with a singular Bessel operator ⋮ On the higher-dimensional harmonic analog of the Levinson \(\log\log\) theorem ⋮ A new Leibniz rule and its integral analogue for fractional derivatives ⋮ An application of the \(N\)-fractional calculus operator method to a modified Whittaker equation ⋮ Bounds for the nonhomogeneous GASPT equation ⋮ ABOUT SOME GENERALIZATIONS OF THE PROPERTIES OF THE ERD´ELYI-KOBER OPERATOR AND THEIR APPLICATION ⋮ Solution of the Cauchy Problem for Generalized Euler-Poisson-Darboux Equation by the Method of Fractional Integrals ⋮ On some generalizations of properties of the Lowndes operator and their applications to partial differential equations of high order

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