A Conformable Fractional Composition Operator and Its Boundedness with Applications

Abstract

It is well known that there is a strong connection between operator theory and complex analysis. The concept of conformable operators is also employed in fractional calculus to define fractional differential and integral operators. In this study, we develop conformable composition operators in a complex domain acting on spaces of analytic functions. The boundedness of weighted composition operators has been extensively studied on various analytic function spaces. The present work investigates the boundedness of two weighted operators with several variable differences on different analytic function spaces, particularly those involving Banach spaces of analytic functions. Our approach is based on the use of Möbius transformations and Green's functions defined in terms of the pseudo-hyperbolic distance.