A Novel of Ω-Proportional Fractional Integrals of a Function with Respect to Another Function

This paper explores a key topic in fractional calculus, which is the sophisticated idea of proportional fractional integrals with regard to another function. Our focus is on synchronous, monotonic, and bounded functions. We investigate the mathematical features and theoretical underpinnings of these integrals. The paper sheds fresh information on the behavior and uses of fractional integrals by concentrating on these particular types of functions, underscoring their potential for modeling intricate systems and processes. The findings provide new approaches for future study and useful applications, expanding our grasp of fractional calculus.