On defining the distributions \(\delta^k\) and \((\delta')^k\) by fractional derivatives

DOI10.1016/j.amc.2014.08.068zbMath1338.46053OpenAlexW2044311469MaRDI QIDQ295239

Changpin Li, Chen Kuan Li

Publication date: 17 June 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.08.068

zbMATH Keywords

distributionneutrix limitdelta sequenceCaputo fractional derivative and generalized Taylor's formuladelta function

Mathematics Subject Classification ID

Distributions and ultradistributions as boundary values of analytic functions (46F20)

Related Items (12)

Defining compositions of \(x_+^\mu\), \(|x|^\mu\), \(x^{-s}\), and \(x^{-s}\ln |x|\) as neutrix limit of regular sequences ⋮ Several results of fractional differential and integral equations in distribution ⋮ Babenko's approach to Abel's integral equations ⋮ Unnamed Item ⋮ The composition of the distributions x−λlnsx− and x+−r/λ ⋮ On defining the distributions \(\delta^{r}\) and \((\delta')^{r}\) by conformable derivatives ⋮ On powers of the compositions involving Dirac-delta and infinitely differentiable functions ⋮ Remarks on fractional derivatives of distributions ⋮ Interpretations of some distributional compositions related to Dirac delta function via Fisher's method ⋮ The fractional Green's function by Babenko's approach ⋮ Remarks on the linear fractional integro-differential equation with variable coefficients in distribution ⋮ Numerical methods for fractional partial differential equations

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• The distributional products on spheres and Pizetti's formula
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• On a Riemann-Liouville generalized Taylor's formula
• On Defining the Convolution of Distributions
• A Commutative Neutrix Product of Distributions on R^m
• On the Distributions δ^k and (δ')^k
• Fractional integrals of generalised functions
• Riemann's Form of Taylor's Series
• Rules for integrals over products of distributions from coordinate independence of path integrals
• Defining the \(k\)th powers of the Dirac-delta distribution for negative integers

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