A simple fractional-calculus approach to the solutions of the Bessel differential equation of general order and some of its applications.

DOI10.1016/j.camwa.2004.09.009zbMath1088.34004OpenAlexW2093487164WikidataQ115359630 ScholiaQ115359630MaRDI QIDQ2387377

Wei-Chich Ling, Katsuyuki Nishimoto, Shy-Der Lin, Hari M. Srivastava

Publication date: 2 September 2005

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2004.09.009

zbMATH Keywords

trigonometric functionsBessel functionsFrobenius methodBessel differential equationgeneralized Leibniz ruleFractional calculuspower-series solutionsIndex lawLinear (ordinary and partial) differential equationslinearity propertydifferentegral equationsFuchsian (and non-Fuchsian) equations

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Linear ordinary differential equations and systems (34A30)

Related Items (12)

Neumann series of Bessel functions ⋮ Explicit solutions of a certain class of associated Legendre equations by means of fractional calculus ⋮ A survey of fractional-calculus approaches to the solutions of the Bessel differential equation of general order ⋮ Explicit solutions of Jacobi and Gauss differential equations by means of operators of fractional calculus ⋮ Some fractional-calculus results involving the generalized Lommel-Wright and related functions ⋮ An operational matrix based on Legendre polynomials for solving fuzzy fractional-order differential equations ⋮ Remarks on a simple fractional-calculus approach to the solutions of the Bessel differential equation of general order and some of its applications ⋮ Solutions in the discrete fractional forms of two differential equations with singular points ⋮ Solutions in the discrete fractional forms of two differential equations with singular points ⋮ Explicit solutions of a certain class of differential equations by means of fractional calculus ⋮ Explicit solutions of singular differential equation by means of fractional calculus operators ⋮ Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments

Cites Work

• Some fractional differintegral equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Explicit solutions of some linear ordinary and partial fractional differintegral equations.
• Certain operators of fractional calculus and their applications to differential equations.
• A certain family of fractional differintegral equations
• A unified presentation of certain families of non-fuchsian differential equations via fractional calculus operators
• Certain classes of ordinary and partial differential equations solvable by means of fractional calculus.
• Some families of ordinary and partial fractional differintegral equations
• An application of the \(N\)-fractional calculus operator method to a modified Whittaker equation
• Solutions of a certain class of fractional differintegral equations
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