Stellar structure via truncated M-fractional Lane-Emden solutions

The Lane-Emden equation (LEE) is essential for modeling the structure of self-gravitating, spherically symmetric polytropic stars in hydrostatic equilibrium. Astronomy commonly employs it to depict normal stars, white dwarfs, and other celestial systems. This paper presents a new formulation of the LEE using truncated M-fractional derivatives (TMD), providing a fractional generalization that expands the conventional comprehension of polytropic gas spheres. Using the accelerated power series approach, we find solutions to the TMD Lane-Emden equation and create polytropic models spanning a variety of polytropic indices. Our results give fundamental insights into stellar properties: whereas the initial zero of the fractional Lane-Emden function grows with decreasing fractional parameters, the radius and mass of polytropic models representing stars like the Sun and white dwarfs decrease under the same circumstances. This mismatch underlines the importance of fractional factors on the structural scaling of stars, offering a broader insight into their physical features. The fractional polytropic models presented here expand the classic theory of polytropes and provide possible applications in comprehending the complex behavior of varied astrophysical phenomena under fractional calculus frameworks.