Remarks on 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.2005.03.021zbMath1105.34002OpenAlexW4210256252WikidataQ115359629 ScholiaQ115359629MaRDI QIDQ2494715

Shy-Der Lin, Pin-Yu Wang, Hari M. Srivastava

Publication date: 30 June 2006

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2005.03.021

zbMATH Keywords

Bessel differential equationoperation of fractional calculus

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Explicit solutions, first integrals of ordinary differential equations (34A05) Linear ordinary differential equations and systems (34A30) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Solutions to PDEs in closed form (35C05)

Related Items (10)

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 ⋮ Integral inequalities of systems and the estimate for solutions of certain nonlinear two-dimensional fractional differential systems ⋮ A new dynamic model of ocean internal solitary waves and the properties of its solutions ⋮ 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 ⋮ Explicit solutions of a certain class of differential equations by means of fractional calculus ⋮ Unnamed Item

Cites Work

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