Narrow Results

In this paper, we explore a broad extension of Minkowski-type inequalities to the left-sided fractal-fractional integral operator. Our findings serve not only to generalize previously established results but also to introduce a significant array of new inequalities applicable to fractal-fractional, fractional, and classical integrals. These results deepen the understanding of fractal-fractional integral operators and expand the scope of their applications across different mathematical frameworks. The study concludes with several practical applications.