Solving Conformable Gegenbauer Differential Equation and Exploring Its Generating Function

• Published in: International journal of applied and computational mathematics Vol. 10; no. 6
• Main Authors: Al-Masaeed, Mohamed Ghaleb, Rabei, Eqab M., Muslih, Sami I., Baleanu, Dumitru
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.12.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Science and Engineering; Differential equations; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Polynomials; Power series; Recursive functions; Theoretical; Gegenbauer differential equation; 33C45; 33E30; Conformable derivative; 44A10; Ultraspherical polynomials
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-024-01796-4

In this manuscript, we address the resolution of conformable Gegenbauer differential equations with an order of α , where α ∈ (0,1). 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. We plot the conformable Gegenbauer functions for different values of α . The results obtained here will lead to the same Gegenbauer polynomials when α goes to 1.