New Approaches to Fractal-Fractional Bullen's Inequalities Through Generalized Convexity

This paper introduces a new identity involving fractal-fractional integrals, which allow us to derive several new Bullen-type inequalities via generalized convexity. This study provides a significant advancement in the area of fractal-fractional inequalities, presenting a range of results not only for fractional integrals and fractal calculus, but also offering a refinement of the well-known Bullen-type inequality. We further explore the connections between generalized convexity and fractal-fractional integrals, showing how the concept of generalized convexity enables the establishment of error bounds for fractal-fractional integrals involving lower-order derivatives, with an emphasis on their applications in various fields. The findings expand the current understanding of fractal-fractional inequalities and offer new insights into the use of local fractional derivatives for analyzing functions with fractional-order properties.