(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we make use of the concept of fractional q-calculus to introduce a novel class of bi-Bazilevic functions involving q-Ruscheweyh differential operator that are subordinate to Legendre Polynomials. This study explores the characteristics and behaviors of these functions, offering estimates for the modulus of the initial Taylor series coefficients a_2 and a_3 within this specific class and its various subclasses. Additionally, the research delves into the traditional Fekete-Szegö functional problem concerning functions f that are part of our newly defined class and several of its subclasses.