The Mu'azu–Bayawa Integral Transform for Some Bessel Functions
DOI:
https://doi.org/10.61952/jlabw.v2i4.655Keywords:
Mu'azu–Bayawa integral transform, Bessel functions, integral evaluation, ordinary differential equations, variable coefficients, applied mathematicsAbstract
In this research, the Mu'azu–Bayawa integral transform was derived and mathematically analyzed in detail, applying it to a selected set of Bessel functions of the first and second kind. The results show that this transform reduces the complexity of these functions into simpler integral forms, facilitating their handling in applied problems. Various applications of this transform were also included, such as evaluating certain complex integrals that are difficult to solve by traditional methods, where closed-form values were obtained using the transform's properties.
Furthermore, the Mu'azu–Bayawa integral transform was successfully used to find analytical solutions to some ordinary differential equations with variable coefficients, which often appear in mathematical modeling of physical and engineering phenomena such as heat transfer and mechanical vibrations. The results demonstrated the effectiveness of this transform in simplifying the equations and converting them into algebraic equations that are easy to solve, followed by returning to the original domain using the inverse transform. This research opens new horizons for using non-conventional integral transforms in applied mathematics and theoretical physics, with the possibility of generalizing the method to other special functions.
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