A survey of fractional-calculus approaches to the solutions of the Bessel differential equation of general order

Wang, Pin-Yu; Lin, Shy‐Der; Tu, Shih-Tong

doi:10.1016/j.amc.2006.09.005

Cited by 6 publications

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“…The main purpose of this section (and Section 7 below) is to follow rather closely and analogously the investigations in (for example) [16], [23], [53], [63] and [64] of solutions of some general families of second-order linear ordinary differential equations, which are associated with the familiar Bessel differential equation of general order ν (cf. [5], Vol.…”

Section: The Classical Gauss and Jacobi Differential Equations Revisitedmentioning

confidence: 99%

An Elementary and Introductory Approach to Fractional Calculus and Its Applications

Srivástava¹

2017

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A b s t r a c t: The subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. It does indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this paper * is to present a brief elementary and introductory approach to the theory of fractional calculus and its applications especially in developing solutions of certain interesting families of ordinary and partial fractional differintegral equations. Relevant connections of some of the results presented in this lecture with those obtained in many other earlier works on this subject will also be indicated.

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