Solving conformable Gegenbauer differential equation and exploring its generating function
Mohamed Ghaleb Al-Masaeed, Eqab.M.Rabei, Sami I. Muslih, and Dumitru, Baleanu
TL;DR
This paper solves the conformable Gegenbauer differential equation, confirms its solutions match power series methods, and introduces new properties, recursive relations, and a generating function for Gegenbauer functions.
Contribution
It provides a novel conformable approach to Gegenbauer equations, including new formulas and properties not previously established.
Findings
Solutions align with power series results
Established conformable Rodriguez's formula
Derived new generating function for Gegenbauer functions
Abstract
In this manuscript, we address the resolution of conformable Gegenbauer differential equations. We demonstrate that our solution aligns precisely with the results obtained through the power series approach. Furthermore, we delve into the investigation and validation of various properties and recursive relationships associated with Gegenbauer functions. Additionally, we introduce and substantiate the conformable Rodriguez's formula and generating function
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Taxonomy
TopicsFractional Differential Equations Solutions · Iterative Methods for Nonlinear Equations · Nonlinear Waves and Solitons