On defining the distributions \(\delta^{r}\) and \((\delta')^{r}\) by conformable derivatives

DOI10.1186/s13662-018-1865-7zbMath1448.26008OpenAlexW2899739559MaRDI QIDQ1715492

Thabet Abdeljawad, Fahd Jarad, Dumitru Baleanu, Yassine Adjabi

Publication date: 4 February 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-018-1865-7

zbMATH Keywords

distributiongeneralized functionsneutrix limitgeneralized Taylor formuladelta sequenceDirac delta functionconformable derivativeneutrix

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Operations with distributions and generalized functions (46F10) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Distributions and generalized functions on nonlinear spaces (46T30) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Real-valued functions on manifolds (58C05)

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Cites Work

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• On defining the distributions \(\delta^k\) and \((\delta')^k\) by fractional derivatives
• On conformable fractional calculus
• Fractional Newton mechanics with conformable fractional derivative
• Introduction to the neutrix calculus
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Fundamental results of conformable Sturm-Liouville eigenvalue problems
• General conformable fractional derivative and its physical interpretation
• A new definition of fractional derivative
• Time-space fabric underlying anomalous diffusion
• Neutrices
• Delta-convergent sequences that vanish at the support of the limit Dirac delta function
• On the Distributions δ^k and (δ')^k
• Defining the \(k\)th powers of the Dirac-delta distribution for negative integers