Fractional derivatives of products of Airy functions

DOI10.1016/j.jmaa.2007.03.098zbMath1141.33002OpenAlexW2037013846MaRDI QIDQ2382739

Vladimir V. Varlamov

Publication date: 2 October 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.03.098

zbMATH Keywords

fractional derivativesHilbert transformproducts of Airy functions

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (11)

Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions ⋮ Airy functions and Riesz fractional trigonometric operators ⋮ Fractional Ostrovsky Equation ⋮ Some integral identities for products of Airy functions using integral transforms ⋮ Riesz potentials for Korteweg-de Vries solitons and Sturm-Liouville problems ⋮ Integral representations for products of Airy functions and their application for analysis of the Green’s function for a particle in a uniform static field ⋮ Macdonald's identities and integral representations of products of Airy functions ⋮ Integral representations of products of airy functions related to fractional calculus ⋮ Differential and integral relations involving fractional derivatives of Airy functions and applications ⋮ Random fractional generalized Airy differential equations: a probabilistic analysis using mean square calculus ⋮ Riesz potentials for Korteweg-de Vries solitons

Uses Software

• Wolfram Functions Site

Cites Work

• Semi-integer derivatives of the Airy functions and related properties of the Korteweg-de Vries-type equations
• Moment integrals of powers of Airy functions
• Integral representations for products of Airy functions. II: Cubic products
• Integral representations for products of Airy functions. III: Quartic products
• An integral representation for the product of Airy functions
• The Wright functions as solutions of the time-fractional diffusion equation.
• Cauchy problem for the Ostrovsky equation
• On the (generalized) Korteweg-de Vries equation
• Integral representations for products of Airy functions
• Oscillatory integrals generated by the Ostrovsky equation
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• High-frequency refraction and diffraction in general media
• ON THE NATURE OF THE SPECTRUM IN PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS (II)
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